HELP System of particles problem

[Kudo Shinichi]

HELP!System of particles problem

Homework Statement

A 10kg dog walks 3m on a 20kg boat towards shore. How much nearer the shore does the dog end up if the boat was initially at rest.

The Attempt at a Solution

I am not really sure how to approach this problem. I think that the dog is 3 meters closer to the shore, because the boat stays at rest while the dog moves toward the shore...yet I think this is wrong because it is too simple as a physics problem...

Can anyone help me with this problem? thank you very much.

 

[jr01]

hey, here's how i solved this question...not sure if its right. I think we're in the same class

Pi=Pf

m1v1=m2v2

v=d/t

(m2= 20kg + 10kg because the boat and the dog are the same mass once the dog stops moving)

10(3/t) = 30(d/t)

The t's then cross out

30=30d

d=30/30

d= 1.0m

 

[thomate1]

I can say that this problem involves the principles of conservation of momentum and Newton's laws of motion. By walking on the boat, the dog exerts a force on the boat and causes it to move in the opposite direction. This results in a change in the momentum of the boat-dog system. However, since the boat is initially at rest, the total momentum of the system must remain constant. This means that the dog's momentum must be equal and opposite to the boat's momentum.

To solve this problem, we can use the equation: m1v1 + m2v2 = m1v1' + m2v2', where m1 and m2 are the masses of the dog and the boat respectively, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities. Since the boat is initially at rest, v2 = 0.

We can rearrange the equation to solve for the final velocity of the dog, v1':

v1' = (m2v2 - m1v1) / m1

Substituting the given values, we get:

v1' = (20kg * 0m/s - 10kg * v1) / 10kg

Simplifying, we get:

v1' = -v1

This means that the final velocity of the dog is equal in magnitude but opposite in direction to its initial velocity. Therefore, the dog ends up 3m closer to the shore, as initially thought.

In conclusion, this problem highlights the importance of understanding the principles of conservation of momentum and Newton's laws of motion in solving physics problems. I hope this explanation helps in your understanding of the problem.