Dog walking on a raft on water then suddenly halting

[totallyclone]

Homework Statement

A dog of mass 10.0kg is standing on a raft so that he is 20.0m from shore. He walks 8.00m along the raft towards shore and then halts. The raft has a mass of 40.0kg, and we can assume there is no friction between the raft and the water. How far is the dog from shore when he stops?

Homework Equations

E_K=1/2 mv²

The Attempt at a Solution

This is a really tricky question and I'm not quite sure how to proceed. I know that when the dog halts, the raft moves forward towards the shore?

 

[phinds]

What's tricky about it? What external force would cause the raft to have a net movement?

 

[totallyclone]

What's tricky about it? What external force would cause the raft to have a net movement?

I find this question tricky because maybe I'm overthinking it...

I think the external force would be what the dog applies. Then suddenly stopping, transfers the energy to the raft causing it to more forward towards the shore?

 

[phinds]

I find this question tricky because maybe I'm overthinking it...

I think the external force would be what the dog applies. Then suddenly stopping, transfers the energy to the raft causing it to more forward towards the shore?

How is the dog external? What is the dog acting on that is external to the raft?

 

[Nickie]

But I'm not sure how to calculate the distance the dog has moved or the velocity of the raft. Any suggestions?



I would approach this problem by first defining the system and identifying the relevant equations. In this case, the system includes both the dog and the raft, and the relevant equation would be the conservation of momentum. Since we are assuming no friction, we can also use the conservation of energy equation.

Using the conservation of momentum, we can set the initial momentum of the system (when the dog is at rest on the raft) equal to the final momentum of the system (when the dog halts and the raft moves forward).

Initial momentum = Final momentum
(10.0kg)(0m/s) + (40.0kg)(0m/s) = (10.0kg)(v) + (40.0kg)(v)

Solving for v, we get v = 0.4m/s, which is the velocity of the raft after the dog halts.

Next, we can use the conservation of energy equation to determine the distance the dog has moved. The initial energy of the system (when the dog is at rest on the raft) is equal to the final energy of the system (when the dog halts and the raft moves forward).

Initial energy = Final energy
(1/2)(10.0kg)(0m/s)^2 + (1/2)(40.0kg)(0m/s)^2 = (1/2)(10.0kg)(v)^2 + (1/2)(40.0kg)(v)^2

Solving for v again, we get v = 0.4m/s. This means that the dog has moved a total distance of 8.8m (8.0m + 0.4m) from its initial position of 20.0m from shore when it halts.

Therefore, the dog is 11.2m from shore when it stops. This calculation assumes that the dog and the raft are moving in a straight line towards the shore. If the motion is not in a straight line, more information would be needed to accurately calculate the distance from shore when the dog stops.