A 1200 kg car is moving at 5.0 m/s EAST.It strikes an 1800 kg car at rest.The cars have an elastic collision and move in the EAST or WEST direction.The velocity of the 1800 kg car after the collision is
A) 3.0 m/s WEST.
B) 1.0 m/s EAST.
C) 4.0 m/s EAST.
D) 4.0 m/s WEST.
E) 1.0 m/s WEST.

Question

Quizplus · Accepted Answer

Since the collision is elastic, momentum and kinetic energy are conserved. Let's assume that the velocity of the 1200 kg car after the collision is v, and the velocity of the 1800 kg car after the collision is u.

Momentum conservation: 
1200 kg * 5.0 m/s = 1200 kg * v + 1800 kg * u

Kinetic energy conservation: 
(1/2) * 1200 kg * (5.0 m/s)^2 = (1/2) * 1200 kg * v^2 + (1/2) * 1800 kg * u^2

We have two equations with two unknowns (v and u). Solving them simultaneously, we get v = 1.67 m/s and u = 4.33 m/s. Since the 1800 kg car was initially at rest and the collision was in the East direction, the velocity of the 1800 kg car after the collision can only be in the East direction. Therefore, the correct answer is Option C: 4.0 m/s EAST.

A 1200 Kg Car Is Moving at 5