A40-kg canoe carrying two people is at rest on the surface of a lake. one of the people is a 50-kg person who is sitting 1.5 m to the left of the center of mass (cm) of the canoe. the other person has 90 kg and is sitting 0.5 m to the right of the cm of the canoe.

at one point in time, the two people rearrange themselves so that the 90-kg now sits 1.0 m to the left of the cm of the canoe, and the 50-kg person is sitting 0.75 m to the right of the cm of the canoe.

by how much, and in what direction, did the canoe move as a result of this rearrangement? ignore any friction between the canoe and the water.

1.67 m towards right

Explanation:

Let the position of the center of mass of the canoe be at the origin

= mass of canoe = 40 kg

= position of center of mass of canoe = 0 m

= mass of person on left = 50 kg

= position of center of mass of person on left = - 1.5 m

= mass of person on right = 90 kg

= position of center of mass of person on right = 0.5 m

Position of center of mass of the system is given as

After the two people rearrange their positions, we have

= mass of canoe = 40 kg

= position of center of mass of canoe

= mass of person on left = 50 kg

= position of center of mass of person on left = - 1 m

= mass of person on right = 90 kg

= position of center of mass of person on right = 0.75 m

Position of center of mass of the system remains at the same location and is given as

Distance traveled by the canoe is given as

direction of movement : towards right.