Boat moves 0.7m when Juliet walks across it—how does that work?

[Satoy]

I've got most of the problem completed but I need a little help on the last little bit. Julet moves across the boat 2.7m to romeo to give him a kiss. Romeo and the boat weigh 157 kg and Julet weighs 55 kg. How far does the boat move. The boat is at rest before hand.

The answer is .7m and I have no idea how the book got that.

 

[Doc Al]

Hint: If you assume that the water exerts no (horizontal) force on the boat, then the center of mass of the "boat + Romeo + Juliet" cannot move.

 

[Satoy]

Oh ok you just put me in the right state of mind, I got it now.

 

[Satoy]

Let me see if I am right the F to move Juliet needs to be applyed to the total system right?

 

[dextercioby]

Yes.From there,the answer is simple to find.

Daniel.

 

[Doc Al]

Let me see if I am right the F to move Juliet needs to be applyed to the total system right?

Not sure what you are saying here. The net force on the total system is zero.

Think like this. Before Juliet moves, the center of mass of the total system is at some point on the boat. Mark that point with an X. When Juliet moves, where is the new center of mass with respect to that X?