Two ice skaters want to prove the conservation of momentum. Skater A has a mass of 72 kg, and Skater B has a mass of 55 kg. They are originally at rest. They hold hands and face each other. They then push off each other and move in opposite directions. Skater B moves with a velocity of 3.0 m/s. What must the velocity of skater A be in the opposite direction after the push in order to prove the conservation of momentum?
4.0m/s
2.3 m/s
1.5 m/s
2.0 m/s
2.3 m/s
To prove the conservation of momentum, the total momentum before the push must be equal to the total momentum after the push.
Initial momentum = 0 (since both skaters are at rest)
Final momentum = (mass of skater A x velocity of skater A) + (mass of skater B x velocity of skater B)
Let vA be the velocity of skater A after the push.
72kg x vA = 55kg x 3.0m/s
72vA = 165
vA = 165 / 72
vA ≈ 2.3 m/s
Therefore, skater A must have a velocity of 2.3 m/s in the opposite direction after the push in order to prove the conservation of momentum.