A tennis ball of mass mt is held just above a basketball of mass mb and radius R

Question

A tennis ball of mass mt is held just above a basketball of mass mb and radius Rb, as shown in the figure. With their centers vertically aligned, both are released from rest at the same moment, so that the bottom of the basketball falls freely through a height h and strikes the floor. Assume an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down because the balls have separated a bit while falling. The two balls meet in an elastic collision. To what height does the tennis ball rebound? (Use any variable or symbol stated above along with the following as necessary: g.)

Explanation / Answer

the basketball comes to a complete halt when the tennis ball hits it. This is what will happen if the basketball is exactly 3 times the mass of the tennis ball ( and if the collision is elastic. Just assume this. Also assume that the collision of the basketball with the ground is elastic. All this means that the height energy lost by both balls is converted into KE of the tennis ball only and then converted back into GPE of the tennis ball. Total energy of the falling balls = ( Mb + Mt ) . g . H becomes total height energy of the tennis ball = Mt . g . H new H new = (Mb + Mt ) H / Mt No need to actually work out any velocities

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