A small and a large sphere, of mass M and 3M respectively, are arranged as shown on the left side of the figure above. The spheres are then simultaneously
dropped from rest. When the large sphere strikes the floor, the spheres have
fallen a height H. Assume air resistance is negligible. Express all answers in
terms of M, H, and fundamental constants, as appropriate.
a) Derive an expression for the speed vb with which the large sphere
strikes the floor.
Immediately after striking the floor, the large sphere is moving upward with speed vb and collides head-on with
the small sphere, which is moving downward with identical speed vb at that instant. Immediately after the
collision, the small sphere moves upward with speed vs and the large sphere has speed vL
.

b) Derive an equation that relates vb, vs and vL
.

In this particular situation vL = 0.
c) Use your relationship from part (b) to determine the speed of the small sphere in terms of vb.
d) Indicate whether the collision is elastic. Justify your answer using your results from parts (b) and (c).
e) Determine the height h that the small sphere rises above its lowest position, in terms of the original
height H.