A 4.0 kg object is moving at 5.0 m/s NORTH. It strikes a 6.0 kg object at rest. The objects collide elastically and move away 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

First, we need to use conservation of momentum to find the velocity of the system after the collision:

Initial momentum = m1v1 + m2v2 = (4 kg)(5 m/s) + (6 kg)(0 m/s) = 20 kg m/s

Final momentum = m1v1' + m2v2' (where v1' is the final velocity of the 4.0 kg object and v2' is the final velocity of the 6.0 kg object)

Since the objects move away from each other in the NORTH or SOUTH direction, we know that the final velocity of the 6.0 kg object must be 0 m/s (since it was at rest initially and cannot move in a direction opposite to the 4.0 kg object). Therefore, we can simplify the final momentum equation:

Final momentum = m1v1' = (4 kg)(v1')

Now we can use conservation of momentum to solve for the final velocity:

Initial momentum = Final momentum
20 kg m/s = (4 kg)(v1')
v1' = 5 m/s

Since the 4.0 kg object was originally moving in the NORTH direction, and the objects move away from each other either NORTH or SOUTH, the final velocity of the 4.0 kg object must also be in the NORTH or SOUTH direction. Since the 6.0 kg object cannot move in the SOUTH direction, the 4.0 kg object must move in the SOUTH direction. Therefore, the final velocity of the 4.0 kg object is 1.0 m/s SOUTH.

So the correct answer is C: 1.0 m/s SOUTH.

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