Walking in a Boat (Center of Mass?)

[PrideofPhilly]

Homework Statement

A(n) 64 kg boat that is 8 m in length is initially 8.5 m from the pier. A 32 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the turtle.

Assume: There is no friction between boat and water.

How far is the child from the pier when she reaches the far end of the boat?

Homework Equations

I am not quite sure if this is a Center of Mass question, but if it is the equation is:

X = m1*x1 + m2*x2/m1 + m2
m = mass
x = distance

The Attempt at a Solution

I really don't know where to begin with this problem. I just need a little push or hint to catalyst the problem solving process.

I understand that when the child is at the far end of the boat he will be 16.5 m away from the pier, but I'm not sure what to do next.

 

[LowlyPion]

Figure that since there is no friction, there is no external force, so the center of mass of both won't change.

Now figure where the center of mass is originally with respect to the center of mass of just the boat. With the child at the other end, how much must the center of mass of the boat shift to account for the change in the position of the child. That distance is how much nearer the pier the boat will move.

 

[nlightner]

I would first try to visualize the situation and understand the forces at play. In this case, we have a boat with a mass of 64 kg and a child with a mass of 32 kg. The boat is initially at a distance of 8.5 m from the pier, and the child moves to the far end of the boat which is 8 m in length.

To solve this problem, we can use the concept of center of mass. The center of mass is the point at which the entire mass of an object can be considered to be concentrated. In this case, the center of mass of the boat and child together can be calculated using the equation given in the problem.

We know that the center of mass of the boat and child combined will be somewhere along the length of the boat. Since the boat is initially 8.5 m from the pier and the child moves to the far end of the boat, we can assume that the center of mass will also move towards the far end of the boat. This means that the distance between the center of mass and the pier will decrease.

To calculate the distance between the child and the pier when the child reaches the far end of the boat, we can use the following equation:

X = (m1*x1 + m2*x2)/(m1 + m2)

Where m1 is the mass of the boat, m2 is the mass of the child, x1 is the initial distance between the boat and the pier, and x2 is the distance between the child and the pier.

Plugging in the values from the problem, we get:

X = (64*8.5 + 32*8)/(64 + 32) = 8.17 m

Therefore, when the child reaches the far end of the boat, they will be 8.17 m away from the pier. This calculation takes into account the movement of the center of mass of the boat and child combined as the child moves to the far end of the boat.

In summary, by using the concept of center of mass, we can calculate the distance between the child and the pier when the child reaches the far end of the boat. This approach can be used to solve many problems involving the movement of objects with varying masses.