Question

Two men (A and B), having weights of 120lbs. and 150lbs., respectively, stand on a 300lb. cart initially at rest. Each runs at a speed of 5 ft/s relative to the cart. Determine the final speed of the cart if man A runs and jumps off, causing the cart to move with man B, and then man B jumps off the same end.

Answer 1

Let be the mass of A and be its relative velocity wrt cart.

Let be the mass of B and be its relative velocity wrt cart.

Let be the mass of cart and be its velocity when A jumps off and be it velocity when B jumps off. Initially it had 0 velocity.

Then from momentum conservation

After A jumps off we have

.......1

After B jumps off, we have

........2

Solving the equations simultaneously we get

Now lighter A jumps first and then heavier B jumps so

This is the final velocity.