Question Detail
Question
A 0.15 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.80 m/s. It has a head-on collision with a 0.30 kg glider that is moving to the left with a speed of 2.20 m/s. Find the final velocity of each glider if the collision is elastic.
Correct Answer
Option A is the correct answer.
Detailed Explanation
For an elastic collision in one dimension, both momentum and kinetic energy are conserved. Let m₁ = 0.15 kg, v₁i = +0.80 m/s; m₂ = 0.30 kg, v₂i = -2.20 m/s. Using the elastic collision formulas: v₁f = [(m₁-m₂)/(m₁+m₂)]v₁i + [2m₂/(m₁+m₂)]v₂i = (0.15-0.30)/(0.45) + (0.60)/(0.45) = (-0.333)(0.80) + (1.333)(-2.20) = -0.2664 - 2.933 = -3.199 ≈ -3.2 m/s. v₂f = [2m₁/(m₁+m₂)]v₁i + [(m₂-m₁)/(m₁+m₂)]v₂i = (0.30)/(0.45) + (0.15)/(0.45) = (0.667)(0.80) + (0.333)(-2.20) = 0.5336 - 0.7326 = -0.199 ≈ 0.20 m/s (to the right).
Hint
Apply conservation of momentum and conservation of kinetic energy for elastic collisions.