A 49.0 kg person is standing in a canoe while it moves forward at a constant speed of 7.40 m/s. He jumps off the canoe, and just after the jump he has a speed of 1.20 m/s in the same direction he was moving. Just after the jump, the canoe has a speed of 12.5 m/s. What is the mass of the canoe? 59.6 kg 21.2 kg 11.5 kg 4.70 kg

This problem can be solved using the principle of conservation of momentum. The total momentum before the person jumps is equal to the total momentum after the jump.

The total momentum before the jump is the sum of the momentum of the person and the momentum of the canoe. The momentum of an object is calculated as the product of its mass and its velocity. So, the total momentum before the jump is:

Momentum_before = (mass_person * velocity_person) + (mass_canoe * velocity_canoe)

Given that the mass of the person is 49.0 kg and the velocity of the canoe and the person is 7.40 m/s, the equation becomes:

Momentum_before = (49.0 kg * 7.40 m/s) + (mass_canoe * 7.40 m/s)

After the jump, the person and the canoe have different velocities. The total momentum after the jump is:

Momentum_after = (mass_person * velocity_person_after) + (mass_canoe * velocity_canoe_after)

Given that the velocity of the person after the jump is 1.20 m/s and the velocity of the canoe is 12.5 m/s, the equation becomes:

Momentum_after = (49.0 kg * 1.20 m/s) + (mass_canoe * 12.5 m/s)

According to the principle of conservation of momentum, Momentum_before = Momentum_after. Therefore, we can set the two equations equal to each other and solve for the mass of the canoe:

(49.0 kg * 7.40 m/s) + (mass_canoe * 7.40 m/s) = (49.0 kg * 1.20 m/s) + (mass_canoe * 12.5 m/s)

Solving this equation for mass_canoe gives the mass of the canoe as 59.6 kg.