How Does the Center of Mass Stay Constant When a Child Walks on a Boat?

[to4u]

I'm not the brightest physics student, so I probably just overlooked something obvious...please help!

Problem:

A 40 kg child stands at one end of a 70 kg boat that is 4 meters in length. The boat is initially 3 meters from the pier. The child notices a turtle on a rock near the far end of the boat and proceeds to walk to that end to catch the turtle. Neglecting friction b/w the boat and water...

a. describe motion

I said that the child moves to the right and the boat to the left...but center of mass stays same


b. where is the child relative to the pier when he reaches far end of the boat?

I set...

x(child intial)*m(child)+x(boat initial)*m(boat) / m(child)+m(boat) = x(child final)*m(child)+x(boat final)*m(boat) / m(child)+m(boat)

the denominators cancel so...

40*x(child initial) + 70*x(boat initial) = 40*x(child final) + 70*x(boat final)

so here's my question...how do I solve this without knowing how much the boat moved after the child walked to the other side of the boat? Is the x(child initial)= -2 m (2 m left of center of mass) or 3 m (from pier)? And what about the boat?



Your help is much appreciated!

 

[mjsd]

you need a set of coordinates (of frame of reference) for you system. The pier is basically your origin (if you want), the boat has a center of mass somewhere relative to the pier, the child will have a CM relative to the pier, then the system as a whole (child + boat) will have a CM relative to the pier. movment of the child changes the child's CM and hence boat's CM has to change accordingly so that the CM of whole system remain the same. All these can be done relative to the pier