Collision Theory

We need to find the percentage loss of energy after the ball rebounds to of its original height. Step 1: Determine the initial and final energies. The ball is dropped from height . Initial energy (just before collision) is: After collision, it rebounds to . Final energy (at the top of the rebound): Step 2: Calculate the fraction of energy retained. Step 3: Calculate the percentage loss of energy. Fraction of energy lost: Final Answer:

Let the masses of the bodies be . Let the initial velocities be and . Let the final velocities be and . Coefficient of restitution . Since the masses are equal, we can use the following simplified equations for one-dimensional elastic collisions: and If we use and , then . Using Conservation of momentum: so . . So so so and . Also, from conservation of momentum, , so . Solving for and , we get and . The ratio of velocities is .