Question

A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...

Answer 1

Draw a diagram to illustrate the problem as shown below.
Each ball has mass = m.
The initial velocity of the blue ball = u.
The initial velocity of the red ball = 0.

Initial total momentum is
P1 = m*u + m*0 = mu
Final momentum is
P2 = mv + 3mv = 4mv

Because momentum is conserved,
mu = 4mv
u = 4v

Answer:
The velocity of the blue ball before the collision is 4v.