How far will the raft move (center of mass problem)?

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In summary, a 32 kg boy standing on a 59 kg raft walks from a point 1.0 m from the left edge of the raft to a point 1.0 m from the right edge of the raft, causing the raft to move a distance of 2.33 meters. The calculation was done using the equation x = (m1x1 + m2x2) / (m1+m2).
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Homework Statement



A 32 kg boy is standing on a 59 kg raft that is 8 m wide. He walks 6 m from a point 1.0 m from the left edge of the raft to a point 1.0 m from the right edge of the raft. If you ignore resistance of the water to the motion of the raft, how far does the raft move during this procedure

Homework Equations



x = (m1x1 + m2x2) / (m1+m2)

The Attempt at a Solution



x1 = (m1x1 + m2x2) / (m1+m2)
x1 = (32(1) + 59(4)) / (91)
x1 = 2.725

x1 = (m1x1 + m2x2) / (m1+m2)
x1 = (32(7) + 59(4)) / (91)
x1 = 5.055

x = 5.055 - 2.725
x = 2.33m

but it's wrong. anyone can help?
 
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nvm it was just a mis calculation, I got it now, thanks
 

Related to How far will the raft move (center of mass problem)?

1. How does the center of mass affect the movement of a raft?

The center of mass is the point where the weight of an object is evenly distributed. In the case of a raft, the location of the center of mass will determine how the raft moves in the water. If the center of mass is closer to the front of the raft, it will tend to move forward. Similarly, if the center of mass is closer to one side, the raft will move in that direction.

2. What factors affect the distance the raft will move?

The distance the raft will move is affected by several factors, including the weight and distribution of objects on the raft, the shape and size of the raft, the speed of the current, and the presence of any obstacles in the water.

3. How can I calculate the center of mass of a raft?

To calculate the center of mass of a raft, you will need to know the weight and location of each object on the raft. Using the formula for center of mass, which is the sum of the individual masses multiplied by their distances from a reference point, divided by the total mass of the system, you can determine the center of mass of the raft.

4. Will the center of mass always be in the center of the raft?

No, the center of mass may not always be in the center of the raft. It depends on the weight and location of objects on the raft. For example, if there is a heavier object on one side of the raft, the center of mass will be shifted towards that side.

5. Can the center of mass change as the raft moves?

Yes, the center of mass can change as the raft moves. As objects on the raft shift or are added or removed, the center of mass will also shift. This can affect the movement of the raft in the water.

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