Two ice skaters suddenly push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s relative to the ice. What speed does the 60-kg skater acquire relative to the ice?
A) 0.50 m/s
B) 0.38 m/s
C) 0.00 m/s
D) 0.28 m/s
E) 0.75 m/s

Question

Two ice skaters suddenly push off against one another starting from a stationary position. The 45-kg skater acquires a speed of  0.375 m/s relative to the ice. What speed does the  60-kg skater acquire relative to the ice?
A)  0.50 m/s
B)  0.38 m/s
C)  0.00 m/s
D)  0.28 m/s
E)  0.75 m/s

Quizplus · Accepted Answer

The law of conservation of momentum states that the total momentum of a closed system is constant if no external forces are acting on it. Since the skaters push off against each other from a stationary position, their initial total momentum is 0. For the 45-kg skater with a speed of 0.375 m/s, their momentum is $45 \times 0.375 = 16.875$ kg·m/s. To conserve momentum, the 60-kg skater must have the same magnitude of momentum but in the opposite direction, so their speed $v$ is found by $60v = 16.875$, giving $v = 16.875 / 60 = 0.28125$ m/s, which rounds to 0.28 m/s.

Two Ice Skaters Suddenly Push Off Against One Another Starting