Question

a boy is running to the east and jumps into a stationary boat in a lake. once the boy lands in the boat, the boat moves to the east. which best compares the initial momentum of the boy with the final momentum of the boy/boat system? the initial momentum of the boy is zero because the velocity cancels with the mass of the boy. the initial momentum of the boy is greater than the boy/boat because the boy has a greater velocity than the boat. the initial momentum of the boy is less than the boy/boat because the boy has less mass than the boat. the initial momentum of the boy is equal to the boy/boat because the final velocity of the boat is less than the initial velocity of the boy.

Explanation:

Step1: Recall the law of conservation of momentum

In the absence of external horizontal forces (assuming no water - resistance etc. in the horizontal direction), the total momentum of a closed system is conserved. The system here consists of the boy and the boat. The initial momentum of the system is just the momentum of the boy (since the boat is stationary, its initial momentum is 0). The final momentum of the system is the combined momentum of the boy and the boat moving together.

Step2: Analyze the conservation of momentum

According to the law of conservation of momentum $p_{i}=p_{f}$, where $p_{i}$ is the initial momentum of the system and $p_{f}$ is the final momentum of the system. The initial momentum of the system is the momentum of the boy $p_{boy - initial}=m_{boy}v_{boy}$, and the initial momentum of the boat $p_{boat - initial}=m_{boat}\times0 = 0$. The final momentum of the system $p_{final}=(m_{boy}+m_{boat})v_{final}$. Since there are no external horizontal forces, $m_{boy}v_{boy}=(m_{boy}+m_{boat})v_{final}$.

Answer:

The initial momentum of the boy is equal to the boy/boat because of the law of conservation of momentum in the absence of external horizontal forces. So the correct option is: The initial momentum of the boy is equal to the boy/boat because the final velocity of the boat is less than the initial velocity of the boy.