1.) You are playing with carts in lab. while your lab instructor isn't looking, you carefully attach a spring-loaded plunger on the end of a 0.25kg cart and push it at a velocity of +20m/s relative to the earth. It collides with a 0.5kg cart traveling at +10m/s relative to the earth. the collision triggers the plunger, causing an explosive collision between them. If you know the system's kinetic energy is increased by 25% in the collision in the earth's frame of reference, what are the final velocities of the carts in this reference frame?
2.) You and your friends are playing soccer. Your friend kicks a soccer ball at 8m/s toward you. Instead of kicking it like normal, you decide to kick a slightly larger ball at it to make it reverse directions. They hit head on with a coefficient of restitution of .9.
a.) If the soccer ball has an inertia of 600g, how fast would the larger, 750g, ball have to be traveling 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 is convertible to some other form?
d.) What are the final velocities of both of the balls immediately after the collision?