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?
The conservation of momentum states that the total momentum before an interaction is equal to the total momentum after the interaction.
The total momentum before the interaction is:
0 = 0
After they push off each other, Skater A's momentum (m1v1) will be equal in magnitude but opposite in direction to Skater B's momentum (m2v2).
So the equation we can set up is:
m1v1 = -m2v2
Substitute the given values:
72kg * v1 = -55kg * 3.0 m/s
Solving for v1:
v1 = -55kg * 3.0 m/s / 72kg
v1 = -2.29 m/s
Therefore, Skater A must move in the opposite direction with a velocity of 2.29 m/s in order to prove the conservation of momentum.