Question

A 2130 kg car, moving at 21.5 m/s, runs into a car that has a mass of 2240 kg

and is moving at 11.4 m/s in the same direction. The cars stick together after
the collision. Assuming momentum is conserved, what is their final velocity?
OA. 14.1 m/s
OB. 12.5 m/s
O C. 16.3 m/s
O D. 19.4 m/s

Answer 1

C. 16.3 m/s

Step-by-step explanation:

You want to know the final velocity of the combined mass of a 2130 kg car at 21.5 m/s after collision with a 2240 kg car at 11.4 m/s in the same direction. Momentum is conserved.

Momentum

The momentum of each object is the product of its mass and velocity. When momentum is conserved, the momentum of the mass after the collision is the same as that before the collision.

m1·v1 +m2·v2 = (m1 +m2)·v3

Then the velocity after the collision is ...

v3 = (m1·v1 +m2·v2)/(m1 +m2)

You may recognize this as the weighted average of the initial velocities, where the weights are the respective masses of the objects.

v3 = (2130·21.5 +2240·11.4)/(2130 +2240) ≈ 16.3

The final velocity is 16.3 m/s, matching choice C.