Two ice skaters are at rest and facing each other. One skater weighs 140 lbs and the other skater weighs 180 lbs. The skaters "push off" of each other. The 140 lb skater then moves away at 5.00 m/s to the EAST. What is the velocity of the 180 lb skater?
A) 6.50 m/s EAST
B) 6.50 m/s WEST
C) 3.89 m/s EAST
D) 3.89 m/s WEST
E) 1.55 m/s EAST

Question

Quizplus · Accepted Answer

According to the law of conservation of momentum, the total momentum before the push off is zero, and the total momentum after the push off is also zero. Therefore, the momentum of the 140 lb skater to the East must be balanced by the momentum of the 180 lb skater to the West, and the magnitudes of the momenta must be equal. Let v be the velocity of the 180 lb skater. Then, using the conservation of momentum:

momentum of 140 lb skater = momentum of 180 lb skater

(140 lbs)(5.00 m/s) = (180 lbs)(-v)

Solving for v, we get:

v = - 3.89 m/s

The negative sign means that the 180 lb skater is moving to the West. Therefore, the answer is D) 3.89 m/s WEST.

Two Ice Skaters Are at Rest and Facing Each Other