Question

two billiard balls have velocities of 2.0 m/s and -1.0 m/s when they meet in an elastic head-on collision. What is the final velocity of the first ball after collision?

Answer 1

Since masses are equal

( u1 + u2 ) = (v1 + v2)

2-1 = 1 = (v1+v2) ----------------1

Since the collision is elastic

(u1² + u2²) = (v1² + v2²)
4 +1 = 5 = v1² + v2²

From 1,
v1² + (1-v1) ² = 5
v1² + (1-2v1 + v1²) = 5
v1² -v1 - 2 = 0

v1 = -1 or 2

Since 2 is not given in the choice,
the answer is -1m/s