Two billiard balls have velocities of 4.0 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?
A)+1.0 m/s
B)-1.0 m/s
C)-3.0 m/s
D)+5.0 m/s
E)+4.0 m/s

Question

Two billiard balls have velocities of 4.0 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?
A)+1.0 m/s
B)-1.0 m/s
C)-3.0 m/s
D)+5.0 m/s
E)​+4.0 m/s

Quizplus · Accepted Answer

In an elastic head-on collision, the total momentum before the collision equals the total momentum after the collision. We can use the formula: 
m1v1i + m2v2i = m1v1f + m2v2f 
where m is the mass and v is the velocity.

Substituting the given values, we get: 
m1v1i + m2v2i = m1v1f + m2v2f 
m1 = m2 (since the balls are identical) 
4.0 m/s * 1kg + (-1.0 m/s * 1 kg) = 1kg * v1f + 1kg * (-1.0 m/s)
3.0 kg m/s = 1kg * v1f - 1kg
4.0 kg m/s = 1kg * v1f 
v1f = 4.0 m/s / 1kg = 4.0 m/s/kg = +4.0 m/s

However, we need to consider the direction of the velocity. The first ball initially had a positive velocity, and the second ball initially had a negative velocity. Since they collided head-on, the first ball will rebound with a negative velocity. Therefore, the final velocity of the first ball is -1.0 m/s.

Two Billiard Balls Have Velocities of 4