**Challenge Problem: Free Fall**Click here to see the solution

Three spheres are held at at various positions above a table. Sphere 1 is closest to the table, sphere 3 is furthest from the table. Assume all collisions with the table are perfectly elastic. That is, no energy is lost upon impact and the sphere returns to its initial height before it falls again as if it was dropped from rest. Consider motion up away from the table to be positive motion.

For questions A and B assume the following:

Sphere 1 initial height = 2.0 m

Sphere 2 initial height = 3.0 m

Sphere 3 initial height = 4.0 m

Sphere 1 is released from rest.

A. At what speed must sphere 2 be initially traveling upward if it first hits the table at the same time that sphere 1 hits the table for a second time?

B. At what speed must sphere 3 be initially traveling downward if it first hits the table at the same time that sphere 1 hits the table for the first time?

C. Now assume that the initial upward speed of sphere 2 is 1 m/s and the initial upward speed of sphere 3 is 2 m/s, determine the difference in initial heights of spheres 2 and 3 if they hit the table for the first time when sphere 1 hits the table for the sixth time. Sphere 1 is released from rest.