You and your friends are playing soccer. Your friend kicks a 600g soccer ball at 8m/s towards you. Instead of kicking it like normal, you decide to kick a slightly larger 750g ball at it to make it reverse directions. They hit head-on with a coefficient of restitution of 0.9.
a) How fast would the larger ball have to be travelling to exactly reverse the soccer ball's velocity?
b) What is the initial relative velocity of the two objects?
c) What percentage of the original kinetic energy of the system is convertible to some other form?
d) What are the final velocities of the balls immediately after the collision?