Robert and his younger brother Jake decide to go fishing in a nearby lake. Just

Question

Robert and his younger brother Jake decide to go fishing in a nearby lake. Just before they cast off, they are both sitting at the back of the boat and the bow of the boat is touching the pier. Robert notices that they have left the fishing bait on the pier and asks Jake to go get the bait. Jake has a mass of 61.5 kg and an arm reach of 50.0 cm, Robert has a mass of 87.5 kg, and the boat has a mass of 84.0 kg and is 2.70 m long. Determine the distance the boat moves away from the pier as Jake walks to the front of the boat. Ignore any friction between the boat and the water. It should also be noted that since the boat is not symmetrical, the center of mass of the boat is not at the midpoint of the length of the boat.

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Explanation / Answer

let x be the center of mass of system

let l be the distance of center of mass of boat from pier

x = (m1*2.7 + m2*2.7 + m3*l)/(m1+m2+m3)

after the boat moves a distance x1

x = (m1*(2.7+x1) + m2*x1 + m3*(l+x1) )/(m1+m2+m3)

(m1*2.7 + m2*2.7 + m3*l)/(m1+m2+m3) = (m1*(2.7+x1) + m2*x1 + m3*(l+x1) )/(m1+m2+m3)

(m1*2.7 + m2*2.7 + m3*l) = (m1*(2.7+x1) + m2*x1 + m3*(l+x1) )

(87.5*2.7 + 61.5*2.7 + 84*l) = (87.5*(2.7+x1) + (61.5*x1) + (84*(l+x1))

x1 = 0.713 m <<<-----ANSWER

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