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

Let the car be mass m1 = 800 kg and the truck be mass m2 = 1200 kg. Using conservation of momentum:

m1 v1i + m2 v2i = m1 v1f + m2 v2f

Solve for v2f:

v2f = (m1 v1i + m2 v2i − m1 v1f) / m2
= (800·30 kg·m/s + 1200·20 kg·m/s − 800·23 kg·m/s) / 1200 kg
= (24000 + 24000 − 18400) kg·m/s / 1200 kg
= 29600 kg·m/s / 1200 kg
= 74/3 m/s ≈ 24.67 m/s.

So the truck is traveling about 24.67 m/s after the collision.