a 3.7 kg dog stands on a 19 kg flatboat at distance D = 6.1 m from the shore. It walks 2.6 m along the boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore.
_ _ _ _ _ _ m
To find how far the dog is from the shore after it walks 2.6 m along the boat, we can use the principle of conservation of momentum.
The total momentum before and after walking can be assumed to be zero, since there is no external force acting on the system. The momentum of the dog is given by the product of its mass and velocity, and the momentum of the boat is given by the product of its mass and velocity.
Before the dog walks, the initial momentum of the system is:
Momentum_before = (mass of dog) x (velocity of dog) + (mass of boat) x (velocity of boat)
The dog is initially at rest, so its velocity is zero. The boat is also initially at rest, so its velocity is zero. Therefore, the initial momentum of the system is zero.
After the dog walks, the final momentum of the system is:
Momentum_after = (mass of dog) x (velocity of dog) + (mass of boat) x (velocity of boat)
Since the dog stops after walking, its velocity becomes zero. The velocity of the boat remains zero. Therefore, the final momentum of the system is also zero.
Setting the initial and final momenta equal to each other, we get:
0 = (mass of dog) x 0 + (mass of boat) x 0
This equation indicates that the initial and final momenta are equal to zero. Since the mass and velocity of both the dog and the boat are positive, the only way for the equation to be true is if both the mass and velocity are zero.
Therefore, the distance of the dog from the shore after it walks 2.6 m along the boat is the same as the initial distance, D = 6.1 m.
So, the dog is then 6.1 m from the shore.
boats distance: 3.7/19 * 2.6
Work this out. THe center of gravity stays the same place.