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?

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.

The total momentum before the jump is the sum of the momentum of the person and the momentum of the canoe. Momentum is calculated as the product of mass and velocity.

Momentum of the person before the jump = mass of the person * velocity of the person = 53.0 kg * 7.90 m/s = 418.7 kg*m/s

The total momentum before the jump is also the sum of the momentum of the person and the momentum of the canoe after the jump.

Momentum of the person after the jump = mass of the person * velocity of the person = 53.0 kg * 1.70 m/s = 90.1 kg*m/s

Let's denote the mass of the canoe as m. The momentum of the canoe after the jump is m * 12.6 m/s.

So, the total momentum after the jump is 90.1 kg*m/s + m * 12.6 m/s.

According to the principle of conservation of momentum, the total momentum before the jump is equal to the total momentum after the jump. Therefore, we can set up the following equation:

418.7 kgm/s = 90.1 kgm/s + m * 12.6 m/s

Solving this equation for m gives:

m = (418.7 kgm/s - 90.1 kgm/s) / 12.6 m/s = 26.1 kg

So, the mass of the canoe is approximately 26.1 kg.