Question

Two ice skaters want to prove conservation of momentum. Skater A has a mass of 72kg, and Skater B has a mass of 48kg. They are originally at rest. They hold hands and face each other. They then push off each other and move in opposite directions. Skater moves with a a velocity of 5m/s. What must the velocity of skater A be in the opposite direction after the push in order to prove conservation of momentum?2m/s 2m/s 4.5 m/s 4.5 m/s 8m/s 8m/s 3.3 m/s

Answer 1

To prove the conservation of momentum, the total momentum before and after the push must be equal.

The initial momentum is given by:
Initial momentum = (mass of skater A x velocity of skater A) + (mass of skater B x velocity of skater B)
Initial momentum = (72 kg x 0 m/s) + (48 kg x 0 m/s) = 0 kg.m/s

The final momentum is given by:
Final momentum = (mass of skater A x velocity of skater A) + (mass of skater B x velocity of skater B)
Final momentum = (72 kg x velocity of skater A) + (48 kg x 5 m/s)

Since the total momentum is conserved, the final momentum must be equal to the initial momentum:
0 kg.m/s = (72 kg x velocity of skater A) + (48 kg x 5 m/s)

Simplifying the equation:
-(48 kg x 5 m/s) = 72 kg x velocity of skater A
-240 kg.m/s = 72 kg x velocity of skater A
-240 kg.m/s / 72 kg = velocity of skater A
-3.33 m/s ≈ velocity of skater A

Therefore, the velocity of skater A in the opposite direction after the push must be approximately -3.33 m/s in order to prove conservation of momentum.