What is the velocity of the first ball after the collision?

Question

A 5-kg ball moving at 6 m/s collides with a 1-kg ball at rest. The balls bounce off each other and the second ball moves in the same direction as the first ball at 10 m/s.

Answer 1

Assuming an elastic collision where kinetic energy and momentum are conserved, the answer is the following:

m₁v_1i + m₂v_{2i =} m₁v_{1f +} m₂v_2f -----> v₁f = -v₁i((m₂v_2f/m₁v_1i) - 1) Plug in numbers ----> v_1f = 4 m/s.