A 4.0 kg object is moving at 5.0 m/s NORTH.It strikes a 6.0 kg object at rest.The objects have an elastic collision and move in the NORTH or SOUTH direction.The velocity of the 4.0 kg object after the collision is
A) 1.0 m/s NORTH.
B) 4.0 m/s NORTH.
C) 1.0 m/s SOUTH.
D) 4.0 m/s SOUTH.
E) 0 m/s.

Question

Quizplus · Accepted Answer

In an elastic collision, momentum and kinetic energy are conserved. Let's call the initial velocity of the 4.0 kg object "v1" and the final velocity of the 4.0 kg object "v2".

Momentum before the collision = Momentum after the collision
(4.0 kg)(5.0 m/s) = (4.0 kg)(v2) + (6.0 kg)(0 m/s)
20 kg m/s = 4v2
v2 = 5 m/s

Since the collision is elastic, kinetic energy before the collision = kinetic energy after the collision.
(1/2)(4.0 kg)(5.0 m/s)^2 = (1/2)(4.0 kg)(v2)^2 + (1/2)(6.0 kg)(0 m/s)^2
50 J = 10J + 0J
v2 = sqrt(40/4) = sqrt(10) = 3.16 m/s

Therefore, the final velocity of the 4.0 kg object is 3.16 m/s SOUTH (since the collision was in the NORTH direction). The best answer choice is C: 1.0 m/s SOUTH, since it is the closest to the actual answer. Answer choices A and B are both in the NORTH direction, which is incorrect. Answer choice D is too large, and answer choice E is not a valid option.

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