Two ice skaters want to prove conservation of momentum. Skater A has a mass of 72 kg, and skater B has a mass of 48 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 m/s.
What must the velocity of skater A be in the opposite direction after the push in order to prove conservation of momentum?
(1 point)
Responses
1.5 m/s
1.5 m/s
4.5 m/s
4.5 m/s
2.0 m/s
2.0 m/s
3.0 m/s
Using the principle of conservation of momentum, the initial momentum of the system (before the push) is equal to the final momentum of the system (after the push).
The initial momentum is the sum of the individual momenta of each skater, which can be calculated as:
momentum_A_initial = mass_A * velocity_A_initial
Since both skaters are originally at rest, the initial velocity of skater A is 0 m/s. Therefore, momentum_A_initial = 72 kg * 0 m/s = 0 kg·m/s.
The final momentum is the sum of the individual momenta of each skater after the push. The momentum of skater B can be calculated as:
momentum_B_final = mass_B * velocity_B_final
Plugging in the given values, momentum_B_final = 48 kg * 3 m/s = 144 kg·m/s.
Since momentum is conserved, the sum of the initial momenta must equal the sum of the final momenta. Therefore:
momentum_A_initial + momentum_B_initial = momentum_A_final + momentum_B_final
0 kg·m/s + 0 kg·m/s = momentum_A_final + 144 kg·m/s
Simplifying the equation:
144 kg·m/s = momentum_A_final
Therefore, the momentum of skater A after the push must be 144 kg·m/s.
To calculate the velocity of skater A, we can rearrange the equation for momentum:
momentum_A_final = mass_A * velocity_A_final
144 kg·m/s = 72 kg * velocity_A_final
Dividing both sides of the equation by 72 kg:
2 m/s = velocity_A_final
Therefore, the velocity of skater A in the opposite direction after the push must be 2 m/s.