Question

A 59.0 kg person is standing in a canoe while it moves forward at a constant speed of 9.90 m/s. he jumps off the canoe, and just after the jump he has a speed of 2.20 m/s in the same direction he was moving. just after the jump, the canoe has a speed of 12.8 m/s. what is the mass of the canoe?

Answer 1

The mass of the canoe is approximately 37.93 kg.

Step-by-step explanation:

To solve this problem, we can apply the principle of conservation of momentum. The momentum of an object is given by its mass multiplied by its velocity. Before the person jumps off the canoe, the total momentum of the system (person + canoe) is equal to the product of the mass of the person and the velocity of the canoe. After the person jumps off, the total momentum is the sum of the momentum of the person and the momentum of the canoe.

Let's represent the mass of the canoe as 'm'.

Using the principle of conservation of momentum:

(mass of person)(velocity of canoe) = (mass of person)(velocity of person) + (mass of canoe)(velocity of canoe)

(59.0 kg)(9.90 m/s) = (59.0 kg)(2.20 m/s) + (m)(12.8 m/s)

Solving for 'm', we get:

m = ((59.0 kg)(9.90 m/s) - (59.0 kg)(2.20 m/s)) / (12.8 m/s)

m = 37.93 kg

Therefore, the mass of the canoe is approximately 37.93 kg.