Long Answer. Please Answer the following questions, showing all work. Thank You!

1. A 65 kg man standing on a 130 kg boat jumps off the boat towards the dock at a speed of 2 m/s. What is the resulting speed of the boat?

1. A 100 kg cannon is sitting on a frictionless surface as it fires a cannonball horizontally at 40 m/s. If the cannon's recoils backwards at a speed of 2 m/s, what was the mass of the cannonball?

1. Two carts are sitting on a frictionless track with a compressed spring between them. The sum of the masses of carts A and B is 1.5 kg. After the spring releases, Cart B has twice the speed of Cart A. What is the mass of each cart?

1. A child in a boat throws a 6.40kg package out horizontally with a speed of 10.0m/s. Calculate the velocity of the boat immediately after the throw, assuming it was initially at rest. The mass of the child and the boat together is 71kg. Ignore water resistance.