A 53.0 kg person is standing in a canoe while it moves forward at a constant speed of 7.90 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.70 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 12.6 m/s. What is the mass of the canoe? 19.2 kg 69.9 kg 24.8 kg 7.15 kg
Question
A 53.0 kg person is standing in a canoe while it moves forward at a constant speed of 7.90 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.70 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 12.6 m/s. What is the mass of the canoe? 19.2 kg 69.9 kg 24.8 kg 7.15 kg
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the jump is equal to the total momentum after the jump.
Before the jump, the total momentum (P_before) is the sum of the momentum of the person and the momentum of the canoe. The momentum of an object is its mass times its velocity, so:
P_before = (mass_person * velocity_person) + (mass_canoe * velocity_canoe)
Substituting the given values:
P_before = (53.0 kg * 7.90 m/s) + (mass_canoe * 7.90 m/s)
After the jump, the total momentum (P_after) is the sum of the momentum of the person and the momentum of the canoe:
P_after = (mass_person * velocity_person) + (mass_canoe * velocity_canoe)
Substituting the given values:
P_after = (53.0 kg * 1.70 m/s) + (mass_canoe * 12.6 m/s)
According to the principle of conservation of momentum, P_before = P_after. Therefore, we can set the two equations equal to each other and solve for the unknown mass of the canoe:
(53.0 kg * 7.90 m/s) + (mass_canoe * 7.90 m/s) = (53.0 kg * 1.70 m/s) + (mass_canoe * 12.6 m/s)
Solving this equation for mass_canoe gives the mass of the canoe as 24.8 kg. So, the correct answer is 24.8 kg.
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