Question

A 5.00-kg ball, moving to the right at a velocity of +2.00 m/s on a frictionless table, collides head-on with a stationary 7.50kg ball. find the final velocities of the ball if the collision is elastic

Answer 1

Using the law of conservation of momentum:
m₁u₁ + m₂u₂ = m₁v₁ + m₂ v₂; u₂ = 0
5 x 2 = 5v₁ + 7v₂
10 = 5v₁ + 7v₂
v₂ = (10 - 5v₁)/7
Elastic collision so kinetic energy conserved:
1/2 x 5 x 2²  = 1/2 (5v₁² + 7v₂²)
20 = 5v₁² + 7((10 - 5v₁)/7)²
140 = 35v₁² + 5v₁² + 100 - 20v₁
40v₁² - 20v₁ - 40 = 0
v₁ = 1.28 m/s OR v₁ = -0.78 m/s
The first ball is lighter so its velocity will change direction due to collision.
v₁ = -0.78 m/s

10 = 5(-0.78) + 7v₂
v₂ = 1.98 m/s