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
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
