In figure (a), a 4.0 kg dog stands on a 17 kg flatboat at distance D = 6.1 m fro
ID: 1289551 • Letter: I
Question
In figure (a), a 4.0 kg dog stands on a 17 kg flatboat at distance D = 6.1 m from the shore. It walks 2.2 m along the boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore.
______m
In figure (a), a 4.0 kg dog stands on a 17 kg flatboat at distance D = 6.1 m from the shore. It walks 2.2 m along the boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then from the shore. ______mExplanation / Answer
There is no net force on the system, so the center of mass remains where it was at the beginning:
M*?x = 0 = mb*?xb + md*?xd (mb and md = mass of boat and dog, xb abd xd = distance moved)
---> |?xb| = md/mb*|?xd|
The dog moves 2.2 m relative to the boat.
the dog moves into one direction, the boat into the other:
|?xb| + |?xd| = 2.2 --> substitute ?xb from above:
md/mb*|?xd| + |?xd| = 2.2 --> solve for ?xd:
|?xd| = 2.2/(1 + md/mb) = 2.2/(1 + 4/17) = 1.780 -->
The dog stands 2.2 closer to the shore than before = 6.1 -1.780 m
= 4.32 m = answer