A 57.0 kg person is standing in a canoe while it moves forward at a constant speed of 10.0 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.80 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 13.1 m/s. What is the mass of the canoe? 7.83 kg 33.1 kg 29.1 kg 151 kg
Question
A 57.0 kg person is standing in a canoe while it moves forward at a constant speed of 10.0 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.80 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 13.1 m/s. What is the mass of the canoe? 7.83 kg 33.1 kg 29.1 kg 151 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_initial) is the sum of the momentum of the person and the momentum of the canoe. The momentum of an object is given by the product of its mass and its velocity. So,
P_initial = (mass of person * velocity of person) + (mass of canoe * velocity of canoe)
Substituting the given values,
P_initial = (57.0 kg * 10.0 m/s) + (mass of canoe * 10.0 m/s)
After the jump, the total momentum (P_final) is the sum of the momentum of the person and the momentum of the canoe. So,
P_final = (mass of person * velocity of person) + (mass of canoe * velocity of canoe)
Substituting the given values,
P_final = (57.0 kg * 1.80 m/s) + (mass of canoe * 13.1 m/s)
According to the principle of conservation of momentum, P_initial = P_final. So, we can set the two equations equal to each other and solve for the mass of the canoe:
(57.0 kg * 10.0 m/s) + (mass of canoe * 10.0 m/s) = (57.0 kg * 1.80 m/s) + (mass of canoe * 13.1 m/s)
Solving this equation for the mass of the canoe, we get:
mass of canoe = [(57.0 kg * 10.0 m/s) - (57.0 kg * 1.80 m/s)] / (13.1 m/s - 10.0 m/s)
mass of canoe = 33.1 kg
So, the mass of the canoe is 33.1 kg.
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