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Question

A man weighing 60 kg is standing on a flat boat so that he is at a distance of 10 m from the shore. The boat weighs 20 kg and there is no friction between it and the water. If the man walks 4 m relative to the boat towards the shore and stops, then how far is the man from the shore?

A
1 m
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B
7 m
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C
3 m
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D
9 m
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Solution

The correct option is D 9 m
Mass of man(m)=60 kg
Mass of boat(M)=20 kg
Initially, the system is at rest
vCM=0
As there is no external force
vCM=constant=0
Hence displacement of centre of mass,
ΔxCM=0
m1Δx1+m2Δx2m1+m2=0
mΔx1+MΔx2=0 ....(i)
where Δx1= displacement of man w.r.t ground
& Δx2=displacement of boat w.r.t ground

Let the boat move by distance d2 in a direction opposite to man (direction of motion of man is taken +ve)
Hence, Δx2=d2
Since man walks +4 m relative to boat, displacement of man relative to ground
Δx1=4+Δx2=4d2
Substituting in Eq (i):
m(4d2)+M(d2)=0
60(4d2)+20(d2)=0
d2=3 m
Displacement of man towards shore will be:
Δx1=4d2=43=1 m
Man is now at a distance of (101)=9 m from shore.

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