Two ice skaters push off against one another starting from a stationary position.The 45.0-kg skater acquires a speed of 0.375 m/s.What speed does the 60.0-kg skater acquire? Assume that any other unbalanced forces during the collision are negligible.
A) 0.500 m/s
B) 0.281 m/s
C) 0.375 m/s
D) 0.750 m/s
E) 0.000 m/s

Question

Quizplus · Accepted Answer

By conservation of momentum in the x-direction, we have:

(m1)(v1) + (m2)(v2) = 0

where m1 and v1 are the mass and velocity of the 45.0-kg skater, and m2 and v2 are the mass and velocity of the 60.0-kg skater. Initially, both skaters are at rest, so v1 = 0. After the collision, the 45.0-kg skater has a speed of 0.375 m/s. Substituting these values into the equation and solving for v2 gives:

(45.0 kg)(0.375 m/s) + (60.0 kg)(v2) = 0

16.875 + 60v2 = 0

v2 = -0.28125 m/s

The negative sign means that the 60.0-kg skater is moving in the opposite direction to the 45.0-kg skater. Taking the absolute value gives:

|v2| = 0.281 m/s

Therefore, the correct answer is B.

Two Ice Skaters Push Off Against One Another Starting from a Stationary