Conservation of momentum theoretical question

[i_heart_you]

Homework Statement

A tennis ball of mass m is held just above a basketball of mass M. Their
centers are vertically aligned. Both are released at the same moment, and
fall a distance of h until the basketball hits the ground, which it rebounds
from elastically, and then undergoes an elastic collision with the tennis
ball. How high up does the tennis ball go?

Homework Equations

P = mv
E=1/2mv^2 + mgh

The Attempt at a Solution

i figured that since all the collisions in this problem are elastic all the energy is conserved so the tennis ball should technically return to the height that its droped from but I don't think that's the right answer. Please any help would be appreciated!

 

[ehild]

What about momentum? Both balls will have the same velocity before the basketball hits the ground. It will recoil -with what velocity? and collide with the tennis ball, with opposite velocity. Both the momentum and the energy are conserved in this collision. Calculate the velocity of the tennis ball just after collision.

ehild

 

[rl.bhat]

At the instant of collision, the basketball with tennis ball rebounds with the initial velocity. The reaction experienced by them is (M + m)*g. But the net reaction force experienced by tennis ball is (M + m )*g - mg = ma.
Find a and then h..