A 90.0 kg person is sitting in a 100 kg boat, which is floating at rest on a lake. In the boat is a stone with a mass of 5.00 kg. The person throws the stone at 4.00 m/s horizontally in the NORTH direction. The kinetic energy of the boat and person after throwing the stone is
Question
A 90.0 kg person is sitting in a 100 kg boat, which is floating at rest on a lake. In the boat is a stone with a mass of 5.00 kg. The person throws the stone at 4.00 m/s horizontally in the NORTH direction. The kinetic energy of the boat and person after throwing the stone is
Solution
To solve this problem, we need to use the principle of conservation of momentum. The total momentum before the stone is thrown is equal to the total momentum after the stone is thrown.
Before the stone is thrown, the total momentum is 0 because everything is at rest.
After the stone is thrown, the momentum of the stone is its mass times its velocity, which is 5.00 kg * 4.00 m/s = 20.00 kg*m/s.
Because momentum is conserved, the momentum of the person and the boat must be -20.00 kg*m/s (it's negative because it's in the opposite direction of the stone's momentum).
The total mass of the person and the boat is 90.0 kg + 100 kg = 190.0 kg.
So, the velocity of the person and the boat is the momentum divided by the mass, which is -20.00 kg*m/s / 190.0 kg = -0.105 m/s.
The kinetic energy is given by the formula 1/2 * mass * velocity^2.
So, the kinetic energy of the boat and person after throwing the stone is 1/2 * 190.0 kg * (-0.105 m/s)^2 = 1.04 J.
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