Middle School

An 83 kg fisherman jumps from a dock into a 139 kg rowboat at rest on the west side of the dock. If the velocity of the fisherman is 3.1 m/s to the west as he leaves the dock, what is the final velocity of the fisherman and the boat?

Answer in units of m/s.

Answer :

Final answer:

To find the final velocity of the fisherman and the boat, we use the principle of conservation of momentum. By setting the initial momentum equal to the final momentum, we can calculate the final velocity to be 1.38 m/s to the west.

Explanation:

To find the final velocity of the fisherman and the boat, we need to use the principle of conservation of momentum. The momentum before the jump is equal to the momentum after the jump. The momentum of an object is calculated by multiplying its mass by its velocity.

Before the jump, the fisherman's momentum is (83 kg)(3.1 m/s) = 256.3 kg·m/s to the west. The rowboat is at rest, so its momentum is 0.

After the jump, the fisherman and the boat move together with the same final velocity. Let's assume this final velocity is v. The total momentum is now (83 kg + 139 kg)v kg·m/s to the west. Setting the initial momentum equal to the final momentum, we have 256.3 kg·m/s = (83 kg + 139 kg)v kg·m/s. Solving for v, we get v = 1.38 m/s to the west.

Final answer:

The final velocity of the fisherman and the boat is 0 m/s to the west.

Explanation:

To determine the final velocity of the fisherman and the boat, we can use the principle of conservation of momentum.




  3. First, let's calculate the initial momentum of the fisherman and the boat, which will be equal to the final momentum.

  6. The formula to calculate momentum is: momentum = mass x velocity.

  9. Since the boat is at rest initially, its momentum is 0 kg*m/s.

  12. The momentum of the fisherman is: 83 kg x (-3.1 m/s) = -256.3 kg*m/s (negative because it's moving to the west).

  15. The final momentum will be 0 kg*m/s, so the momentum after the fisherman jumps is: 0 kg*m/s.

  18. We can set up an equation using the principle of conservation of momentum: initial momentum = final momentum.

  21. -256.3 kg*m/s + 0 kg*m/s = 0 kg*m/s.

  24. Solving for the final velocity of the fisherman and the boat, we get: final velocity = (final momentum) / (total mass).

  27. The total mass is the sum of the mass of the fisherman and the mass of the boat: total mass = 83 kg + 139 kg = 222 kg.

  30. Substituting the values, the final velocity is: final velocity = 0 kg*m/s / 222 kg = 0 m/s.



Therefore, the final velocity of the fisherman and the boat is 0 m/s to the west.

Other Questions