A ball with a mass of 2 kg is rolling at 2 m/s and elastically collides with a resting ball with a mass of 9 kg. What are the post-collision velocities of the balls?

1 Answer

The initially moving ball would move 1.273 m/s to the left while the ball initially at rest would move 0.72m/s to the right.

Explanation:

(NOTE: velocities with apostrophes denotes the arbitrary object's final velocity )

Consider the total momentum of the system.

mv_1+mv_2 = mv'_1+mv'_2
Note that final velocities are positive because I assumed them to move to the right after the impact.

mv_1+mcancel(v_2) = mv'_1+mv'_2
(2)(2) = (2)(v'_1)+(9)(v'_2 )

Moreover, the problem states that the impact involves an elastic collision. Therefore, the coefficient of restitution of the system, e, is 1.
e = 1=(v'_2-v'_1)/(v_1-v_2) = (v'_2-v'_1)/(2-0)

therefore,2 =v'_2-v'_1

To solve the post-velocities solve the system of equations:
(1) : 9v'_2 +2v'_1=4
(2) : v'_2-v'_1=2

Where v'_1= -1.273
and v'_2 = +0.72

Since v'_1 is negative, the assumed direction of its final velocity is the opposite.