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The rocks all have the same size and shape, but they have different masses. The rocks are all thrown straight up, but with different speeds. The masses of the rocks and their speeds when released are given in the figure. All start from the same height. Neglect air resistance. Rank these rocks on the basis of the maximum height attained.       A B C D E F mass: 1.0 kg 1.1 kg 1.3 kg 2.5 kg 2.8 kg 4.1 kg vi : 2.5 m/s 2.3 m/s 3.8 m/s 2.5 m/s 1.3 m/s 2.7 m/s Notice that the mass of the rocks makes no difference; all rocks (and all other bodies) have the same acceleration (namely, g = 9.8 m/s2)! The maximum height can be found from the "third" of our "big three" Kinematics equations v2 = v2 + 2 a ( s si ) At the top of the flight, each rock stops so v = 0. The acceleration is a = g = 9.8 m/s2. For each si = 0. Therefore v2 = v2 + 2 a ( s si ) 02 = vi2 + 2 a ( s 0 ) s =  s =  s =  A ClarisWorks spreadsheet seems an appropriate way to carry out this calculation six times.  4.13 Shown in the figure are six laboratory carts of varying masses. Each has an initial velocity and a net force as shown in the figure. Rank these carts on the basis of their final velocity after 10 seconds.  From the mass and the net force we can determine the acceleration; F = m a a = F/m =  Once we know the acceleration, we can readily calculate the velocity from v = vi + a t and we want to evaluate this for t = 10 seconds. Again, a ClarisWorks spreadsheet seems an easy way to do this same calculation six times:  4.19 The acceleration of gravity on the Moons surface is about one-eighth what it is on Earths surface. What is the weight on the Moon of an astronaut whose mass is 85 kg? w = mg w = (85 kg) [(9.8 m/s2)(1/8) ] w = 104 N 4.25 A block starts from rest and slides down a frictionless inclined plane that is inclined 20 from the horizontal and is 2.5 meters long. How fast is the block moving as it reaches the bottom?  Choose the xaxis to lie along the plane as shown and then the yaxis must be perpendicular to that. The weight is the force of gravity, directed straight down. Notice that the mass of the block is not stated. That means we will include it only as "m" and expect that it "drops out" of our equations at the end. The normal (or perpendicular) force FN lies in the positive ydirection. We will resolve the weight into its components as shown in the diagram. wx = w sin 20 = m (9.8 m/s2) (0.34) = 3.35 m wy = w cos 20 = m (9.8 m/s2) (0.94) = 9.21 m Now we can apply Newton's Second Law, Fnet = m a But remember, this is a vector equation and, therefore, is merely shorthand notation for Fnet, x = m ax and Fnet, y = m ay Fnet, x = wx = m ax Fnet, y = FN + wy = m ay wx = 3.35 m = m ax FN 9.21 m = m ay = 0 3.35 m = m ax FN 9.21 m = 0 3.35 = ax FNN = 9.21 m ax = 3.35 m/s2 Now that we know the acceleration it is fairly straightforward to find the velocity when the block has started from rest and moved for a distance of 2.5 m down the plane. v2 = vi2 + 2 a ( s si ) v2 = (0)2 + 2 (3.35 m/s2) ( 2.5 m ) v2 = 16.75 m2/s2 v = 4.1 m/s4.31 Four airline baggage carts are coupled as shown in the figure to make a train; each has a mass of 250 kg. Find the force F that must be applied to accelerate this train at 0.8m/s2. Find the tension in each of the three couplings between the baggage carts.  There are several approaches to solving this. The following seems the most direct but others may be moreinstructive. F is the net force applied to the total mass of 4 x 250 kg = 1000kg F = m a F = (1000 kg) ( 0.8 m/s2) = 800 N FAB is the tension in the coupling between carts A and B.  FAB is the net force applied to the remaining mass of 3 x 250 kg = 750 kg FAB = m a FAB = (750 kg) ( 0.8 m/s2) = 600 N FBC is the tension in the coupling between carts A and B.  FBC is the net force applied to the remaining mass of 2 x 250 kg = 500 kg FBC = m a FBC = (500 kg) ( 0.8 m/s2) = 400 N FCD is the tension in the coupling between carts A and B.  FCD is the net force applied to the remaining mass of the last cart 1 x 250 kg = 500 kg FCD = m a FCD = (250 kg) ( 0.8 m/s2) = 200 N At this point, we are done. Yet it is instructive to go back and look at all the forces on at least one of the carts. We might look at cart B,  To the right, there is the force on cart B due to cart A; this is FBA. Acting to the left, there is the force on cart B due to cart C; this is FBC. The net force is the vector sum of those two forces, Fnet = FBA FBC and we have already solved for those forces. Fnet = FBA FBC = 600 N 400 N = 200 N Of course, Fnet = m a (250 kg) a = 200 N a =   a = 0.8 m/s2 And, indeed, that is the acceleration we started with. It is important to carefully define what is "the mass" you are looking at in F = m a and then look at all the forces acting on that mass. 4.34 A 50 ton (50,000 kg) rocket is acted on by an upward thrust of 600 kN. If the rocket is 25 m tall, how long does it require to rise off the launching pad a distance equal to its own height? Always start with a good, clear, detailed freebody diagram:  The net force is the vector sum of these forces, Fnet = 600,000 N 490,000 N = 110,000 N This net force causes the 50,000 kg rocket to accelerate, Fnet = m a  a = 2.2 m/s2 Starting from rest, with vi = 0, and having an acceleration of 2.2 m/s2, how long does it take the rocket to move 25 m? s = si + vi t +  a t2 25 m = 0 + 0 +  (2.2 m/s2) t2 t2 =  s2 = 22.7 s2 t = 4.8 s 4.39 Two small balls of equal mass are connected by a string 1 m long and are laid out on a smooth (ie, frictionless) table with one ball (A) just at the edge of the table and the other ball (B) 1 m from the edge. The table is 0.5 m high. Ball A is nudged gently over the edge of the table, and things begin to happen. a) How much time is required for ball A to strike the floor? b) How much time is required for ball B to strike the floor? c) How far from the base of the table does ball B strike the floor? Good diagrams are always essential and that is certainly true for this situation.  Once ball A goes over the edge, what are the forces on itand on ball B? The table edge acts like a pulley, changing the direction of the force exerted by the string.  Notice that the masses are not given. We know they are equal and that's all. We will merely put the mass of each ball in the equations as "m" and expect that mass to "drop out" of the equations later on. What is the acceleration of the system? That is, what is the vertical acceleration of mass A or the horizontal acceleration of mass B? Since they are connected by a string, the acceleration of the two balls must be the same. We have the forces from the diagram so we can apply Newton's Second Law, F = m a. Applied to mass A, that is Fnet = m g T = m a That is one equation with two unknowns, tension T and acceleration a. We need an additional equation. Applied to mass B, that is Fnet = T = m a We can substitute this back into the equation we found for mass A, m g m a = m a 2 m a = m g a = g / 2 = 4.9 m/s2 The downward acceleration of ball A and the horizontal acceleration of ball B are both 4.9 m/s2. With this acceleration, how long does it take ball A to strike the floor (remember, it started from rest)? s = si + vi t +  a t2 0.5 m = 0 + 0 +  (4.9 m/s2) t2 t2 =  s2 = 0.204 s2 t = 0.45 s Call this time tA. Now, what is going on with ball B?  When ball A strikes the floor, ball B has the same speed, v = vi + a t v = 0 + (4.9 m/s2) (0.45 s) v = 2.21 m/s Once ball A strikes the floor, the string will no longer be taut and the tension in the string will be zero so ball B will continue to move 0.5 m to the end of the table with a constant speed of 2.21 m/s. This will require a time of t1 =  = 0.226 s Now we are back to a projectile motion problem,  Ball B moves horizontally from the table top with speed v = 2.21 m/s. How long does it take to hit the floor? Moving horizontally simply means the initial velocity in the vertical direction is zero. y = yi + vyi t +  ay t2 y = yi + vyi t +  ( g) t22 0 = 0.5 m + (0) t +  ( 9.8 m/s2) t2 4.9 t2 = 0.5 t2 =  = 0.102 s2 t = 0.32 s Let us call this t2; the the total time ttot is ttot = tA + t1 + t2 ttot = 0.45 s + 0.23 s + 0.32 s ttot = 1.0 s c) How far from the base of the table does ball B strike the floor? During this last 0.32 s, ball B continues to move horizontally with the same horizontal velocity, 2.21 m/s so it travels a horizontal distance of x = vx t x = (2.21 m/s) (0.32 s) x = 0.71 m 4.45 A 7-kg package sits on a rough but level floor. The coefficient of sliding friction between the package and the floor is 0.27. A cord is attached to the package and makes an angle of 30 above the horizontal. What must be the tension in the cord to move the package along the surface with an acceleration of 1.0 m/s2?  We must look at all the forces on the package. That means a carefully drawn freebody diagram.  Now we can apply Newton's Second Lawin its component formsto this situation. Fnet, x = Tx Ff = m ax = m a 0.866 T Ff = (7.0 kg) a 0.866 T Ff = (7.0 kg) (1.0 m/s2) 0.866 T Ff = 7.0 N We know the friction force only as Ff = FN = 0.27 FN so we must solve for the normal force FN. We can do this by looking at the y-component of Newton's Second Law, 0.866 T 0.27 FN = 7.0 N Fnet,y = Ty + FN m g = m ay = 0 0.5 T + FN (7.0 kg)(9.8 m/s2) = 0 0.5 T + FN 68.6 N = 0 Now we have our required two equations since we have two unknowns (FN as well as T). FN = 68.6 N 0.5 T 0.866 T 0.27 (68.6 N 0.5 T) = 7.0 N 0.866 T + 0.135 T = 7.0 N + 18.5 N T = 25.5 N 4.48 A man pushes a 20-kg lawn mower at constant speed with a force of 80 N directed along the handle, which makes an angle of 37 with the horizontal. Calculate the following: a) the horizontal and vertical components of the man's force. b) the horizontal retarding force on the mower. c) the normal force between the mower and the lawn (be sure to include the mower's weight). d) the effective coefficient of friction in this case.  Fx = 64 N and Fy = 48 N (the negative sign meaning "down"). b) If the lawn mower moves at constant speed then the net horizontal force on it must be zero so the horizontal retarding force must be 64 N. c) The net vertical force is zero, Fnet, y = FN m g 48 N = 0 FN (20 kg) (9.8 m/s2) 48 N = 0 FN = 196 N + 48 N FN = 144 N d) Ordinarily we describe the friction force in terms of Ff = FN or =  If we consider the horizontal retarding force an effective friction force, then this becomes =  = 0.44 = 0.444.56 A 3.0 kg block is given an initial speed of 1.8 m/s up a plane inclined 20 from the horizontal. The coefficient between block and plane is 0.30. a) How much time is required for the block to slide up the plane and stop? b) How much time is required for the block to slide back down the plane to its initial position? c) What speed does it have as it returns to its initial position?  Carefully construct a free-body diagram of all the forces on the block.  We will take the positive x-axis to lie along the plane, in the direction of the block's intial velocity, and the y-axis to be perpendicular to that. The the net force in the x-direction is Fnet,x = Ff w sin 20 = m a And the net force in the y-direction is Fnet,y = FN w cos 20 = 0 FN = w cos 20 = m (9.8 m/s2) (0.94) = (9.21 m/s2) m Now we can calculate the friction force, Ff = FN = (0.30) (9.21 m/s2) m = (2.76 m/s2) m Now we can use this in Fnet,x = Ff w sin 20 = m a (2.76 m/s2) m m (9.8 m/s2) (0.34) = m a (2.76 m/s22) m m (3.35 m/s2) = m a 2.76 m/s2 3.35 m/s2 = a a = 6.11 m/s2 That is an acceleration down the plane. With that acceleration and the initial speed of 1.8 m/s up the plane, how long does the block slide until it stops, v = vi + a t 0 = 1.8 m/s + ( 6.11 m/s2) t t =  = 0.295 s The block slides up the plane for t = 0.295 s and then comes to rest. In that time, how far has it moved up the plane? v2 = vi2 + 2 a (s si) 0 = (1.8 m/s)2 + 2 ( 6.11 m/s2) s s =  = 0.265 m Now, it begins to slide back down the plane. As the block slides down the plane, the friction force changes its direction. The friction force always opposes the motion. Make a new freebody diagram.  The forces in the ydirection remain the same, Fnet,y = FN w cos 20 = 0 FN = w cos 20 = m (9.8 m/s2) (0.94) = (9.21 m/s2) m As the block moves down the plane, the forces in the xdirection are Fnet,x = + Ff w sin 20 = m a + (0.30) (9.21 m/s2) m m (9.8 m/s2) (0.34) = m a + (0.30) (9.21 m/s2) m m (9.8 m/s2) (0.34) = m a ( 2.76 3.33 ) m/s2 = a a = 0.57 m/s2 The acceleration is still down the plane but it is smaller in magnitude now because of the change in direction of the friction force. Starting from rest, how long does the block require to travel the 0.265 m back to its initial starting position? s = si + vi t +  a t2 0 = 0.265 m + 0 +  ( 0.57 m/s2)t2 t2 =  s2 = 0.93 s2 t = 0.96 s During that time, the block has acquired a velocit>y of v = vi + a t v = 0 + ( 0.57 m/s2) (0.96 s) v = 0.55 m/s That means, with friction present, the motion is not symmetric. The motion down the plane is not the same as the motion up the plane except in the opposite direction. You can tell a difference if a movie of the motion is run in reverse.ZN==DSET.H)@ |:#>O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H)< |:#>O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H>x |:#>|O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H* |:#)8O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H) |:#)O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H* |:#)O6* |D 2 2<% %< <%"d SPNTdSPNT q :#" % P2-v16 - Copyright 1991 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 33 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def mk{md/xl known}{false}ifelse/xk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b p/g{/gf true def}b pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{mk{av 68 gt {false}if}if}b/bps 8 string def/bpm[8 0 0 8 0 0]def/bpp{bps}def/obp{gsave setrgbcolor bps copy pop dup 0 get 8 div floor cvi 8 mul 1 index 2 get 8 div floor cvi 8 mul 2 index 1 get 8 div floor cvi 8 mul 8 4 index 3 get 8 div floor cvi 8 mul{2 index 8 3 index{1 index gsave translate 8 8 scale 8 8 false bpm/bpp load imagemask grestore}for pop}for pop pop pop grestore}b end P2_b pk end{/pat{P2_b gf{end pop sg P2_b mk end{av 68 gt{pop}if}if}{/_pat load end exec}ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg dup 0 ge{/_gr load end exec} {pop end}ifelse}bind def}{/setTxMode{pop P2_b tg dup 0 ge{/_gr load end exec}{pop end}ifelse}bind def}ifelse P2_b xk end{P2_d/_xl/xl load put/xl{P2_b 2 copy P2_tp 4 get add P2_tp 4 3 -1 roll put P2_tp 5 get add P2_tp 5 3 -1 roll put/_xl load end exec}bind def}if}if "h145 113 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "9"180 171 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if " d SPNT d SPNT CdSPNT P2_b 163 142 bb 157 136 151 132 145 142 bc 146 159 154 166 166 170 bc 172 169 187 149 174 143 bc 163 142 bl bx 'p x6 end 52 <4422008844220088>pat P2_b bp &p x6 end 0 pat P2_b 0.25 0.25 bf be end D"D"q9"  !#%&(+.024 5 78997530- *"'"%"""  p9"  !#%&(+.024 5 78997530- *"'"%""" d"SPNT D"d SPNT B"# " d SPNT dSPNTDSET.H*| | ?PO6* |D^^" " "" "xprWEwdxpr "WEWE"WEWEPWEWEp"New Century SchlbkWE q"v,"New Century Schlbk" .  +vWEWE q"i + iWEWE q"2( 2WEWE q"2WE q" ( 2WE q"a) aDSET.H AL |#,?HO6* |D%. .% %." #,"xprWEwdxpr"WEWE",WEWEPWEWEp"New Century SchlbkWE q"v,"New Century Schlbk" .#,#,+vWEWE q"i + iWEWE q"2( 2WEWE q"2WE q" ( 2WE q"() WE q"WE q" )(WE q"gWE q"))  g) )DSET.H )| |#O6* |D^^% % %" #"xprWEwdxpr"WEWE"WEWEPWEWEp"New Century SchlbkWE q"v,"New Century Schlbk" .##+vWEWE q"i + iWEWE q"2( 2WEWE q"2WE q" ( 2WE q"g) gDSET.H ?< |O6* |Djj  " 1"@ 8 "#@" #" !, Geneva .++ A"C ):B" )HC"#"!!(( 1"+*2"G*3"c*4"*5"*6"*7"*8  UUUU CC  ++ GG cc    ,"New Century Schlbk" ((G V(initial))H Height, s(D[m/s)Mm(`)A)52.5)@0.319(|)B)52.3)@0.270()C)53.8)@0.737()D)52.5)@0.319()E)51.3)@0.086(*F)42.7)@0.372 "DSET.H *l |O*XO6* |DQ Q Q"d SPNTdSPNT j+d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.5 m/sd SPNT dSPNT &d SPNT +_F = 1.5 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.1 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,AdSPNTDSET.H ) |O@`O6* |DQ Q Q"d SPNTdSPNT j+d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.5 m/sd SPNT dSPNT &d SPNT +_F = 1.5 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.5 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,BdSPNTDSET.H> |O*O6* |DQ Q Q"d SPNTdSPNT j+d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.3 m/sd SPNT dSPNT &d SPNT +_F = 1.5 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.5 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,CdSPNTDSET.H) |O?O6* |DQ Q Q"d SPNTdSPNT j+d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.3 m/sd SPNT dSPNT &d SPNT +_F = 1.8 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.5 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,DdSPNTDSET.H* |O*pO6* |DQ Q Q"d SPNTdSPNT j+d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.7 m/sd SPNT dSPNT &d SPNT +_F = 2.1 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.8 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,EdSPNTDSET.H) |O*\O6* |DQ Q Q"d SPNTdSPNT j+d SPNT d SPNT B O"4ad SPNT BP)&30d SPNT BP)=3Gd SPNT C 1#".M 8d"SPNT D"d SPNT B"-#"Fd SPNT B"(R##"(udSPNT d SPNT dSPNT &jBd SPNT ,! Avant Garde! .OO+ v = 0.8 m/sd SPNT dSPNT &d SPNT +_F = 1.4 Nd SPNT dSPNT &rIcd SPNT (#id SPNT dSPNT &Id SPNT *- m = 1.2 kgd SPNT dSPNT &d SPNT (3netd SPNT dSPNT &+Ed SPNT (,Fd SPNT dSPNTDSET.H) |*@O6* |D  " "xprWEwdxpr"WEWE" WEWEp"New Century SchlbkWE q"F,"New Century Schlbk" .+ FWEWE q"m(mDSET.H) |O6* |D  "  1 "@ 8  "#@" #" !, Geneva .++ A"C ):B" )HC" )HD" )HE"c )HF"#"! !(( 1"+*2"G*3"c*4"*5"*6"*7"*8"*9   UUUU C C     c c ++ GG cc     ,"New Century Schlbk" ((WFnet)Fmass)Nacc)4 V(initial))Rv(10 s)(DbN)Ekg)>m/s/s)Nm/s)Hm/s(`F/m)v(i)+at(|)A)51.5)H1.1)D1.36)H0.50)D14.14()B)51.5)H1.5)D1.00)H0.50)D10.50()C)51.5)H1.5)D1.00)H0.30)D10.30()D)51.8)H1.5)D1.20)H0.30)D12.30()E)51.8)H2.1)D0.86)H0.70)H9.27(*F)41.4)H1.2)D1.17)H0.80)D12.47 "DSET.H@ |*O6* |D  "dNISI  0,F " adNISI 00,F,"New Century Schlbk" .`+1)ydNISI   O "P#"P#* dNISIdNISI dNISI "ER"ERdNISIdNISI LdNISI  - #dNISI 0-Ϙ+j20dNISI   acu0 "Vcl 7 #dNISI 07}(w = mgdNISI   aIL[`0 Q"J6   c a'0 "L5O  a-A0 "K7V a;$O0 "G7 a0D0 "QRP Uc #dNISI 0UcG(`xdNISI  ;cI"`dNISI 0;cI@(Fdw = w sin 20dNISI  AnO"TddNISI 0AnO9+ xdNISI dNISIdNISI  H"LxdNISI 0HQ(Iw = w cos 20dNISI  Tj"dNISI 0TjJ;+ ydNISI dNISIdNISI   aFZ0 "H< Tj #dNISI 1 Tj J;(UFdNISI  ^%t"adNISI 1^%t C+ NdNISI dNISIDSET.H*T |7J*`O6* |D^^9L L9 9L"d SPNTdSPNT Hbd SPNT d SPNT  7J0.@d SPNT P-7d SPNT P-26;d SPNT d SPNT d SPNT 0L.d SPNT P-P7Zd SPNT P-~6d SPNT d SPNT d SPNT 0.d SPNT P-7d SPNT P-6d SPNT d SPNT d SPNT 0.#d SPNT P-7d SPNT P-6d SPNT d SPNT "$? d SPNT "$ d SPNT "# d"SPNT V&Vd SPNT dSPNT l;l_"$#q8,H%8,8%H8%8dSPNT d SPNT dSPNT &HHbbd SPNT ,! Avant Garde! .7J7J(5Fd SPNT dSPNT &Zt3d SPNT ($Ad SPNT dSPNT &Ysd SPNT (#Bd SPNT dSPNT &Yysd SPNT (#fCd SPNT dSPNT &Z-tGd SPNT ($DdSPNTDSET.H) |7J*LO6* |DLL9L L9 9L"dNISI 7J0.AP-7P-36<0M.P-Q7[P-60.P-7P-6"$@ "$ "# ""t*#*##   #dNISI 0 , Geneva .7J7Eb8(FdNISI  &".dNISI 0&,! Avant Garde! J(#BdNISI  g&r"0dNISI 0g&r(#hCdNISI  '$"0hdNISI 0'$X($DdNISI dNISI  #"1dNISI 1# q(BAdNISI dNISI /;"dNISI 0/; H(0FdNISI dNISI  3#I".0dNISI 13#I ++ ABdNISI  &"GdNISI 1 & ̈(=dNISI DSET.HA| |7*PO6* |D9 9 9" 70.AP-7P-36<0M.P-Q7[P-6"$@ " t(!(!! f&q #dNISI 0f&q,! Avant Garde! .77M+g#CdNISI  '#"0gdNISI 0'#1($DdNISI  "1dNISI 0, Geneva c(FdNISI dNISI  %"0dNISI 1% K+ BCdNISI dNISI "!dNISI 0 *(FdNISI dNISI  %"0dNISI 1% ?+ CBdNISI  "!dNISI 1  (=dNISI dNISIDSET.HAx |7*<O6* |DRR9 9 9"dNISI 70.BP-7P-46="Dt[&l[&[l[[ n{ #dNISI 0n{, Geneva .77+oFdNISI  '$"0odNISI 0'$,! Avant Garde! O($DdNISI dNISI  v$"1dNISI 1v$ E( wCDdNISI dNISI " dNISI 0 4(FdNISI dNISI  $"1dNISI 1$ + DCdNISI  " dNISI 1  q(=dNISI DSET.H*D |7')O6* |D9) )9 9)" 7'0.P-7P-6"# ""t*#*##  #dNISI 0, Geneva .7'7E0+FdNISI  &".dNISI 0&,! Avant Garde! (#BdNISI dNISI  #"0dNISI 1# /(BAdNISI dNISI "dNISI 0 (FdNISI dNISI  #&".dNISI 1#& {q+ ABdNISI  "$dNISI 1  (=dNISI dNISIdNISI  7' "!tq(!!q(!dNISI L *5 #dNISI 0*5 q(+FdNISI dNISI  1#E".+dNISI 11#E `a+ BCdNISI dNISI U`"BdNISI 0U` (VFdNISI dNISI  \#p".VdNISI 1\#p  + CBdNISI  FR"mdNISI 1FR @(G=dNISI dNISIDSET.H*d |/*0O6* |DTT 1 1  1" /"xprWEwdxpr"WEWE" /WEWEp"New Century SchlbkWE q"2WE q"0WE q"0WE q" ,"New Century Schlbk" .//+ 200WE q"N) NWEWE q"2WE q"5WE q"0WE q" (250WE q"kWE q"g) kgDSET.H) |7)O6* |D!9 9! !9" 7"xprWEwdxpr "WEWE"7WEWEp"New Century SchlbkWE q"kWE q"gWE q" WE q"mWE q"/,"New Century Schlbk" .77* kg mWEPWE)%/WE q"s)sWEWEWE q"2 ( 02WEWE q"N (NDSET.H |Z*xO6* |D\ \ \"dNISI  ZP" *`= Z`9*@LZ"5a *0 Z"r@ Za +0 Z"? //B #dNISI 0//B,! Avant Garde! .ZZ+0)Thrust = 600 kN = 600,000 NdNISI  /Y")-dNISI 0/Y*%w = mg = (50,000 kg)(9.8 m/s/s) dNISI  -"0dNISI 0-(.w = 490,000 NdNISI dNISIDSET.H?4 |$*HO6* |D$ $ $" ""xprWEwdxpr" WEWEWEWEp"New Century SchlbkWE q"aWE q" ,"New Century Schlbk" .""*aWE q"=WE q" WE"WE) = WEPWEWE q"F ( FWEWE q"nWE q"eWE q"t + netWEWEWE q"m (mWE q" WE q"=(0 WE q" )=WE"@EWE ) WE q"1WE q"1WE q"0WE q",WE q"0WE q"0WE q"0WE q" ( @110,000WE q"N)4 NWE WE q"5WE q"0WE q",WE q"0WE q"0WE q"0WE q" (A50,000WE q"kWE q"g), kgWE q" WE q"=( WE q" )=WE q"2) WE q".WE q"2WE q" )2.2WE q"mWE q"/) mWEPWE)/WE q"s)sWEWEWE q"2 (2WEDSET.H?, | *8O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H@ | @O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H =@ |=LO6* |D  " "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"2WE q"5,"New Century Schlbk" .+ 25WEWE q"1WE q".WE q"1(1.1DSET.H!@ |=8O6* |D  " 0(2)0202 a bvB0a .0 q $l aL`0aL3`0 .")Vd "z  #dNISI 0,"New Century Schlbk" .+ 1.0 mdNISI  Rca"dNISI 0Rca+Q0.5 mdNISI   P%'-Ph'p #q##dNISIdNISI  8#N #dNISI 18#N( 9AdNISI  ?"U" DdNISI 1?"U(@BdNISI DSET.H"@ |=<O6* |D  "dNISI 0(2+0202 "{ #%*dNISI  DS. #dNISI 1DS.,"New Century Schlbk" .(PAdNISI  y""P$dNISI 1y"m(zBdNISI   "(-dNISIP (PG+O3PHCPLP dNISI a0 " a"<6Q0 1"EF am<Q0 r"QF&  #dNISI 1 (TdNISI  &Q5g"dNISI 1&Q5g+TdNISI  pN"2\dNISI 1pN (|Ow = mgdNISI DSET.H#@ | @O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H$@ | A(O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H%@ |@O6* |D  " "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .+ 1WEWE q"4WE q".WE q"9(4.9DSET.H&) |? O6* |D  "dNISI 0*5C0505# "&PdNISI  G/WF #dNISI 1G/WF,"New Century Schlbk" .k#P(T0AdNISI  ,"T<dNISI 1,F()BdNISI   "*EbdNISIP"*PAJdNISI a# 0 "   #dNISI 1 (vdNISI  Vn"dNISI 1VnO+zvdNISI dNISI Z  aDZ0 "OdNISI  aDZ0aB0 J"c 1 #dNISI 11[(0.5 mdNISI DSET.H')x |:*O6* |D< < <" :"xprWEwdxpr "WEWE" :WEWEp"New Century SchlbkWE q"0WE q".WE q"5WE q" ,"New Century Schlbk" .::+ 0.5WE q"m) mWEWE q"2WE q".WE q"2WE q"1WE q" (2.21WE q"mWE q"/) mWE q"s)/)sDSET.H(* |*O6* |D  "dNISI 0.:)0:0: dNISI  ' #dNISI 1',"New Century Schlbk" .+$BdNISI dNISI  P$$-,dNISI aB3V0 G"'/ F$\ #dNISI 1F$\( GvdNISI dNISI Z  a+0a.E+0 ?":!idNISI  w&M #dNISI 1w&M('0.5 mdNISI   8p`(ZDSET.H)) | *O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H*? | ?0O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H+?$ | ?O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H,Al |?(O6* |D  " "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"0WE q".WE q"5,"New Century Schlbk" .* 0.5WEWE q"4WE q".WE q"9*4.9DSET.H-A\ |WAXO6* |DY Y Y" W """"4HW8 @ 4&,F8"%da 0 W"#L ! #dNISI 0!,"New Century Schlbk" .WW+30dNISI dNISIdNISI  "-dNISI 1 (TdNISI DSET.H.)t |?O6* |D**  "  UUUU0bq 0@H`a$0 "=L ,; #dNISI 0,;,"New Century Schlbk" .+830dNISI dNISI   "GdNISI 1  (TdNISI   a5I0 "?L a$0 ">dNISIdNISI  + @ #dNISI 0+ ((0.5 T = T sin 30 = TdNISI  / "(dNISI 0 /+ydNISI dNISIdNISI   " O @ #dNISI 0O(Pw = m gdNISI dNISI  ??dNISI  /~> @ #dNISI 0/~>(;xdNISI  ";dNISI 0( ydNISI dNISIdNISI  ETl" dNISI 0ETl+DT = T cos 30 = 0.866 TdNISI  JY "`dNISI 0JY+ xdNISI dNISIdNISI   ag{0 "Tq8dNISI  a(m<0 7"jwdNISI L aR0fDB0 ?"\idNISIdNISI  LY @ #dNISI 0LY (VNdNISI  CyR"VdNISI 0CyR (OzFdNISI dNISIdNISI  O3\>"OdNISI 0O3\> (Y4fdNISI  F+UA"Y9dNISI 0F+UA (R,FdNISI dNISIDSET.H/?  |?O6* |D<<  "dNISI   (9(l ooaSq:0 # (oa* _<n] @ #dNISI 0_<n],"New Century Schlbk" .(k=80 NdNISI   a000 ! &o&& a\bpv0 a")l= -< @ #dNISI 0-<(937dNISI  "HdNISI 0($(80 N) cos 37 = (80 N) (0.8) = 64 NdNISI  l{ "*dNISI 0l{(x$(80 N) sin 37 = (80 N) (0.6) = 48 NdNISI dNISIDSET.H0? |?8O6* |D! ! !" "xprWEwdxpr "WEWE"WEWEPWEWEp"New Century SchlbkWE q"F,"New Century Schlbk" .+ FWEWE q"f + fWEWEWEPWEWE q"F (FWEWE q"N + NWEDSET.H1* |*O6* |D  " "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"6WE q"4,"New Century Schlbk" .+ 64WEWE q"1WE q"4WE q"4(144DSET.H2* |KO6* |DM M M"dNISI  K JJ IdNISIdNISI "%+#3#"_ dNISIdNISI a+0 K")d/  @ #dNISI 0,"New Century Schlbk" .KK+ 1.8 m/sdNISI  8G"dNISI 08G+ 720dNISI dNISIDSET.H3* |*O6* |DTT  "dNISI  5n @ "CdNISI 05n,"New Century Schlbk" .+6w = m gdNISI   aCa0 "KQg  h h g #dNISIdNISI "C5#3#":i dNISIdNISI a5I0 "Gn/ 0? #dNISI 00?(<1.8 m/sdNISI  Ve"KdNISI 0Ve+ &20dNISI   a4R0 "GR aRp380 ,"YJ abvA0 "LS` aI$]850 3"KP Ul #dNISI 0Ul (V20dNISI dNISIdNISI  m#|9 @ "idNISI 0m#|9 (y$FdNISI  u,9"y.dNISI 0u,9+ fdNISI dNISIdNISI  Wm"2dNISI 0Wm(XFdNISI  ^m"bdNISI 0^m+NdNISI dNISIdNISI  ye"kdNISI 0ye+k w cos 20dNISI  -<B"fdNISI 0-<B(9 w sin 20dNISI dNISIDSET.H4* |@=\O6* |D,,B B B" @"xprWEwdxpr "WEWE" @WEWEp"New Century SchlbkWE q"1WE q".WE q"8WE q" ,"New Century Schlbk" .@@+ 1.8WE q"mWE q"/) mWE q"s)/)sWEWE q"6WE q".WE q"1WE q"1WE q" (6.11WE q"mWE q"/) mWEPWE)/WE q"s)sWEWEWE q"2 (92DSET.H5* |"HA<O6* |D$J J$ $J" "H"xprWEwdxpr "WEWE"HWEWEPWE WEp"New Century SchlbkWE q"(WE q"1WE q".WE q"8WE q" ,"New Century Schlbk" ."H"H+(1.8WE q"mWE q"/) mWE q"s)/WE q"))s))WEWEWE q"2 ( <2WE q"  + WE WE q"1WE q"2WE q".WE q"2WE q"2WE q" ("12.22WE q"mWE q"/)# mWEPWE)/WE q"s)sWEWEWE q"2 (A2DSET.H6@ |@O6* |D22  "   >"G#2#"= dNISI dNISI aQtg90 "S dNISI L v #dNISI 0v,"New Century Schlbk" .e+20dNISI   a0 "PdNISI  a8Z50 "P'dNISI L (8, #dNISI 0(8,(5FdNISI  1A,"5!dNISI 01A,+ fdNISI  !">%dNISI 0!?(FdNISI  *"dNISI 0*-L+ NdNISI dNISI  "(dNISI 0 d+ w = m gdNISI   a0 "SrdNISI  aA0 "Tj aQg50 "S    #dNISI 0 d(20dNISI  E"dNISI 0E ( w cos 20dNISI  2B"dNISI 02Bt(? w sin 20dNISI dNISIdNISI  Vnh"PdNISI 1Vnh, New YorkŬ(fovdNISI DSET.H7 | <O6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H8=  | =XO6* |D    "  "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"1,"New Century Schlbk" .  * 1WEWE q"2*2DSET.H9= |)O6* |D  " "xprWEwdxpr "WEWE" WEWEp"New Century SchlbkWE q"0WE q".WE q"5WE q"3,"New Century Schlbk" .* 0.53WEWE q"0WE q".WE q"5WE q"7*0.57DSET.H:?@]l8@;6*]lDSET(.H;@d:SSUSp %S @ SSSeS5SP S  S! S!$u S$'E S'`*S*0,S-/S/2S25US5p8%S<<Vp< & @< <<<f<6P<  < < !!< $v$< 'F'`<**0<,-<//<22<5V5p<8&8@<6*]lDSET.H<e*`0=~*`0;;;;;;;;; ; ; ; ; ;;;;;;;DSETT =<(A@l@p@h@L@DK(K N( N & )))PHY 1150, Homework, Chapter 4, page  ZNFNTMCUTSDSUM/Charles E. Miller, Jr.HDNISTYLhA@STYLI>>??>+)\          6            4    "  )           !  #  %  &  (  )  *   +  !,  *"-  #.  D$/  %0  &3  '4 ! (5 " )6 # *7 $ +8 % :,9 & -: ' .; ( /< ) 0= * 1> + 2? , 3@  4A - 5B . 6C / 7D 0 8E 1 9F 2 :G 3 ;H 4 <I - =J 5 >K  ?NK 8@O @HASH"-&* $"-5"-#"-2"-"-"-"- "-"".".$"."/"/""/,#--#-#- 7#-!.#-##-&8#-)=#-0#-56#-9#-<)#-D*#-G0#-M;#-U<#-Vd* d*Ģ* d( %x@%p& Af*?B"-B"-B#-'B#-/B#-$!B#-93B#-; B#-I(B#-O1B#-P9B#-U4B#-W%B#-Z:B#-cB#-g+C(>D* L:Qhjazo}BodN6  CHAR)h    "      #@ @S W     ,3 7VI.@    J</7Z@   :B H (CM@*/HASH   .  ,       &!' )0(15" '/+-.#6$9*;"?4A+B2G-HI L3UY%R CELL)l?"HASH  GRPH)p=fn.HASHogl RULR>@..}$.l...D..}@$.l...D..}$.l...D....$.l...D..@$.l...D..$.l...D..}@..@..dHASH    \Ü^@@^ A  B CP LKUP  "$'1 !"#$%2L&'()*+,-./0123456789:;<=>M?@ $NAMEDefault Default SSHeaderBodyFooterFootnoteFootnote Index DFNTM HelveticaGeneva"New Century SchlbkNew YorkETBL@FNTMCUTSDSUMHDNISTYLETBL