Question

Bumper car A (281 kg) moving +2.82 m/s makes an elastic collision with bumper car B (209 kg) moving -1.72 m/s. What is the velocity of car A after the collision?

Answer 1

Car A after collision: -1.05 m/s

Car B after collision: 2.98 m/s

Answer 2

This is solved in essentially the same way as in your other question [26141465] with some slight differences.

By conservation of momentum,

(281 kg) (2.82 ms⁻¹) + (209 kg) (-1.72 ms⁻¹) = (281 kg) v₁ + (209 kg) v₂

and by conservation of energy,

(281 kg) (2.82 ms⁻¹)² + (209 kg) (-1.72 ms⁻¹)² = (281 kg) v₁² + (209 kg) v₂²

The momentum equation reduces to

432.94 kg•ms⁻¹ = (281 kg) v₁ + (209 kg) v₂

energy equation reduces just as before to

2852.93 J = (281 kg) v₁² + (209 kg) v₂²

Solve for v₁ (same technique as before); you should end up with

v₁ ≈ -1.05 ms⁻¹

and solving for v₂,

v₂ ≈ 3.49 ms⁻¹