Question

A 1200 kg truck is rear-ended by an 800 kg car. Before the collision, the car is traveling at 30 m/s and the truck is going
20 m/s. After the collision the car is traveling 23 m/s. If momentum is conserved, how fast is the truck traveling?
Use units in ALL calculations

Answer 1

Take forward as positive. Momentum is conserved:

Initial momentum = final momentum
800 kg(30 m/s) + 1200 kg(20 m/s) = 800 kg(23 m/s) + 1200 kg(v_truck)

Compute:
800 kg·30 m/s = 24,000 kg·m/s
1200 kg·20 m/s = 24,000 kg·m/s
Total initial = 48,000 kg·m/s

Final: 800 kg·23 m/s = 18,400 kg·m/s

So 48,000 kg·m/s = 18,400 kg·m/s + 1200 kg · v_truck
1200 kg · v_truck = 48,000 − 18,400 = 29,600 kg·m/s

v_truck = 29,600 kg·m/s ÷ 1200 kg = 24.666... m/s ≈ 24.7 m/s

The truck is traveling about 24.7 m/s forward after the collision.