## Two-dimensional Collisions

For collisions in

two dimensions, theconservation of momentumis true foreach component. That is,P_{Tot,i}=P_{Tot,f}is really a

vectorequation and meansP _{Tot,i,x}= P_{Tot,f,x}

andP _{Tot,i,y}= P_{Tot,f,y}For an

inelastic collision, these providetwoequations so we can solve fortwounknowns. Usually this will be thefinal speedand thedirection(orangle) of the final velocity of the two masses that are now stuck together.For an

elastic collisionwe havethreeequations for the Kinetic Energy is also conserved,K _{i}= K_{f}so now we can solve for

three unknowns. This can mean two final speeds and one direction (that is, we must "know" the other direction to solve for the two final speeds and the "other" direction). Or it can mean that we can solve for one final speed and the two final directions (we will need the "other" final speed in order to solve for these three unknowns).

1D CollisionsCenter of MassReturn to ToC, Ch9, Linear Momentum(c) Doug Davis, 2001; all rights reserved