3. Each croquet ball in a set has a mass of 0.50 kg. The green ball, traveling at 12.0 m/s, strikes the blue ball, which is at rest. Assuming that the balls slide on a frictionless
surface and all collisions are head-on, find the final speed of the blue ball in each of
the following situations:
a. The green ball stops moving after it strikes the blue ball.
b. The green ball continues moving after the collision at 2.4 m/s in the
same direction.

a) v_{2f} = 12.0 m / s,  b) v_{2f} = 9.6 m / s

Explanation:

This is an exercise in conservation of momentum, let's start by defining a system formed by the two balls, so that the forces during the collision have been internal and the moment is preserved.

Initial instant. Before the crash

          p₀ = m v₁₀ + m v₂₀

where we use index 1 for the green ball and index 2 for the blue ball.

Final moment. After the crash

         p_f = m v_{1f} + m v_{2f}

the moment is preserved

         p₀ = p_f

         m v₁₀ + m v₂₀ = m v_{1f} + m v_{2f}

they tell us that the blue ball is at rest before the crash

        m v₁₀ = m v_{1f} + m v_{2f}

a) it is indicated that the green ball stops after the collision v1f = 0

        m v₁₀ = m v_{2f}

        v_{2f} = v₁₀

        v_{2f} = 12.0 m / s

b) the speed of the green ball is v_{1f} = 2.4 m / s

         m v₁₀ = m v_{1f} + m v_{2f}

         v_{2f} = v_{1o}- v_{1f}

         v_{2f} = 12.0 - 2.4

         v_{2f} = 9.6 m / s