How Does the Dog's Movement Affect Its Distance from the Shore?

[VitaX]

Homework Statement

A dog with mass 11 kg stands still in a boat with mass 45 kg. the dog is 20 meters from the shore. It then walks 8 meters in the boat towards the shore. how far is the dog from the hore aftter this?

Homework Equations

center of mass equation

The Attempt at a Solution

lets say the dog stands on the boats center of mass. the center of mass is then 0. Now the dog walks 8 meters 1 direction. then the center of mass of the boat has to travel he other direction for the total center of mass to stay the same. So:

11kg*8m+45kg*xm=0

This gives me that boat has traveled 1.95 meters in the opposite direction. So the dog has traveled (8-1.95) meters closer to the shore which gives me that the dog is 13.9 meters away from the shore. The blueprint says 13.6. I just want to know if its me or the blueprint who is wrong here

 

[tiny-tim]

Hi VitaX!

… It then walks 8 meters in the boat towards the shore
…
lets say the dog stands on the boats center of mass. the center of mass is then 0. Now the dog walks 8 meters 1 direction. then the center of mass of the boat has to travel he other direction for the total center of mass to stay the same. So:

11kg*8m+45kg*xm=0

No, that's the formula for the dog walking 8 m relative to the water (or the shore), not relative to the boat.

 

[rl.bhat]

Find the center of mass of dog and boat with respect to the shore. Let d be the distance of the center of gravity of the boat from the shore.
When the dog moves 8 m towards the shore, boat moves x distance away from the shore to keep center of mass in the same position.
Now the distance of the dog and center of gravity of the boat from the shore is (12 + x) m and (d+x) m respectively.
Find the center of mass in this position with respect to the shore and equate it to the previous one. Then solve for x.