A 90 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 5.0 kg. The person throws the stone at 4.0 m/s horizontally in the NORTH direction. The velocity of the person and the boat after throwing the stone is
A) 2.00 m/s NORTH.
B) 1.21 m/s SOUTH.
C) 1.21 m/s NORTH.
D) 0.11 m/s SOUTH.
E) 0.11 m/s NORTH.

Question

Quizplus · Accepted Answer

The principle of conservation of momentum states that the total momentum of a closed system is constant if no external forces are acting on it. Before the stone is thrown, the system (person, boat, and stone) is at rest, so its total momentum is zero. After the stone is thrown, the total momentum must still be zero. The momentum of the stone is given by its mass times its velocity, $5.0 \, \text{kg} \times 4.0 \, \text{m/s} = 20.0 \, \text{kg} \cdot \text{m/s}$ north. To balance this, the boat and the person must have an equal and opposite momentum, which means they move south.The combined mass of the person and the boat is $90 \, \text{kg} + 100 \, \text{kg} = 190 \, \text{kg}$. To find the velocity of the boat and the person, we use the formula for momentum ($p = mv$) and solve for $v$, giving us $v = p/m$. The momentum of the boat and person system must be $20.0 \, \text{kg} \cdot \text{m/s}$ (but in the opposite direction to the stone, hence south), so their velocity is $20.0 \, \text{kg} \cdot \text{m/s} / 190 \, \text{kg} = 0.105 \, \text{m/s}$, which rounds to $0.11 \, \text{m/s}$ south.

A 90 Kg Person Is Sitting in a 100 Kg