Jake attempted to reach the shore of a frozen lake by walking on a plank. The pl

Question

Jake attempted to reach the shore of a frozen lake by walking on a plank. The plank had a mass of 4.50 kg and jake had a mass of 22.0 kg and both were initially at rest. If the plank was 4.0 m in length, pointing directly at the shore, and Jake started at one end of it, how much closer to the shore did he get by walking along the full length of it? Determine this by using the information that the center of mass of the Jake+plank system does not change, so as Jake walks toward the shore the plank moves away from the shore but their center of mass stays in the same place.

Explanation / Answer

centre of mass will remain same so

initial centre of mass=final centre of mass

Let the shore is L m from starting point

initial centre of mass of system=22*L +(4.5*(L-2)/(26.5)=

suppose the plank moves x m

let person moves d m on plank=4

final centre of mass=(22*(L+x-4)+4.5(L-2+x)/(26.5)

Equating both

we got x=3.32 m

Distance from shore=L-4+3.32=L-0.679

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