A 1700 kg car travels at 20 m/s WEST and collides with a 2000 kg car traveling EAST. The collision is completely inelastic and they both come to rest. What was the velocity of the 2000 kg car?
A) 17 m/s EAST
B) 14 m/s EAST
C) 17 m/s WEST
D) 14 m/s WEST
E) 12 m/s EAST

Question

Quizplus · Accepted Answer

In a completely inelastic collision, momentum is conserved. The total momentum before the collision must equal the total momentum after the collision. Since they come to rest after the collision, the total momentum is 0. Let $v$ be the velocity of the 2000 kg car. The momentum of the 1700 kg car is $1700 \times 20 = 34000 \, \text{kg m/s west}$, and the momentum of the 2000 kg car is $2000 \times v$. Setting the total momentum to 0 and solving for $v$ gives $34000 = 2000v$, so $v = 17 \, \text{m/s}$. Since the 1700 kg car was traveling west, for their momenta to cancel out, the 2000 kg car must have been traveling east.

A 1700 Kg Car Travels at 20 M/s WEST and Collides