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?

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.

Step 1: Calculate the total momentum before the jump. The momentum (p) of an object is given by the product of its mass (m) and its velocity (v), p = mv.

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

The person's momentum before the jump is (57.0 kg)(10.0 m/s) = 570 kg*m/s.

We don't know the mass of the canoe yet, so we'll call it m_c. The canoe's momentum before the jump is (m_c)(10.0 m/s) = 10m_c kg*m/s.

So, the total momentum before the jump is 570 kgm/s + 10m_c kgm/s.

Step 2: Calculate the total momentum after the jump.

The person's momentum after the jump is (57.0 kg)(1.80 m/s) = 102.6 kg*m/s.

The canoe's momentum after the jump is (m_c)(13.1 m/s) = 13.1m_c kg*m/s.

So, the total momentum after the jump is 102.6 kgm/s + 13.1m_c kgm/s.

Step 3: Set the total momentum before the jump equal to the total momentum after the jump and solve for m_c.

570 kgm/s + 10m_c kgm/s = 102.6 kgm/s + 13.1m_c kgm/s.

Subtract 10m_c kg*m/s from both sides to get:

570 kgm/s - 102.6 kgm/s = 13.1m_c kgm/s - 10m_c kgm/s.

This simplifies to:

467.4 kgm/s = 3.1m_c kgm/s.

Finally, divide both sides by 3.1 m/s to solve for m_c:

m_c = 467.4 kg*m/s / 3.1 m/s = 150.8 kg.

So, the mass of the canoe is approximately 150.8 kg.