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Question

A rope is stretched between two boats at rest. A sailor in the first boat pulls the rope with a constant force of 100N. First boat with the sailor has a mass of 250kg whereas the mass of second boat is double of that mass. If the initial distance between the boats was 100m, the time taken for two boats to meet each other is:

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A
13.8s
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B
18.3s
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C
3.18s
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D
31.8s
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Solution

The correct option is C 18.3s
Here 100N force acts on both boat.
Thus, 250a1=100a1=0.4m/s2
and 500a1=100a1=0.2m/s2
The relative acceleration ,a=a1(a2)=0.4+0.2=0.6m/s2
Using S=ut+12at2, we get
100=12(0.6)t2 as(u=0)
t=18.3s

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