# Help Conservation of momentum: contestant running on raft. Tough

• nickclarson
In summary, to find the velocity of the contestant relative to the water, you must first find the velocity of the raft which can be done by equating the initial and final momentum of the system. Then, subtract the velocity of the water from the velocity of the contestant to get the final answer.

## Homework Statement

A 62.7-kg woman contestant on a reality television show is at rest at the south end of a horizontal 141-kg raft that is floating in crocodile-infested waters. She and the raft are initially at rest. She needs to jump from the raft to a platform that is several meters off the north end of the raft. She takes a running start. When she reaches the north end of the raft she is running at 4.78 m/s relative to the raft. At that instant, what is her velocity relative to the water?

$$v$$ = velocity of contestant with respect to the water
$$v_{r}$$ = velocity of contestant with respect to the raft
$$V$$ = velocity of raft with respect to the water

$$m$$ = mass of contestant
$$M$$ = mass of raft

## Homework Equations

$$P_{I} = P_{f}$$

$$V=v-v_{r}$$

## The Attempt at a Solution

Here is my derivation and equation but I'm not getting the right answer! Where did I go wrong?

1. $$P_{I} = P_{f}$$

2. $$0=MV+mv$$

We don't know V so I substitute with:

$$V=v-v_{r}$$

3. $$0=M(v-v_{r}) + mv$$

Now solve for v (speed of contestant relative to water)

$$v=\frac{Mv_{r}}{M+m}$$

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Can anybody help? It would be awesome because this is due soon.

I came up with:

$$v=\frac{(M+m)v_{r}}{M+2m}$$

but it gives me the wrong answer.

Not sure what else to do, I swear that equation is correct. I even derived it and compared it to a similar problem in our book and it was very similar! The only difference is that it is asking for the velocity of the raft w/ respect to the water instead of the contestant w/ respect to the water.

This is a lot more simple than it looks. All you have to do is find the velocity of the raft. To do this take the woman's mass multiplied by her velocity (mv) and set it equal to the her mass plus that of the raft times v (m + M)v. So you get mv = (M + m)v. When you put the numbers in you get 62.7kg(4.78m/s) = (62.7 + 141)v

Once you've solved this you get v = 1.47. Since the raft is moving in the opposite direction from the woman v is actually -1.47. To relate this to the water, all you have to do is take the woman's velocity 4.78 m/s and subtract the water's velocity 1.47 m/s. Your answer comes out to 3.31 m/s.

## 1. What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that the total momentum of a closed system remains constant, regardless of any external forces acting on the system.

## 2. How does conservation of momentum apply to a contestant running on a raft?

In this scenario, the contestant and the raft form a closed system. As the contestant runs, they exert a force on the raft, causing it to move in the opposite direction. According to the principle of conservation of momentum, the total momentum of the system remains constant, so the raft will move in the opposite direction with an equal momentum.

## 3. Why is this scenario considered "tough" for conservation of momentum?

This scenario is considered tough because it involves multiple forces acting on the system. The contestant exerts a force on the raft, but the raft also exerts a force on the contestant due to their interaction. Additionally, the water may also exert a force on the raft, creating a more complex system to analyze.

## 4. Can conservation of momentum be violated?

No, conservation of momentum is a fundamental law of physics and cannot be violated. In any closed system, the total momentum will remain constant, even if individual objects within the system may experience changes in momentum.

## 5. How is conservation of momentum related to Newton's third law of motion?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. In the case of the contestant running on the raft, the action is the contestant exerting a force on the raft, and the reaction is the raft exerting an equal force on the contestant. This reaction force is what causes the raft to move in the opposite direction, in accordance with the principle of conservation of momentum.