Question

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

• A. 13.8 s
• B. 18.3 s
• C. 3.18 s
• D. 31.8 s

Answer 1

Answer: (B)

18.3 s

Answer 2

The force of 100 N acts on both the boats

∴ 250a₁ = 100 and 500 a₂ = 100

or a₁ = 0.4 ms^-2

and a₂ = 0.2 ms^-2

Then relative acceleration

= a₁ + a₂ = 0.6 ms^-2

Using S = ut + $\frac { 1 } { 2 }$ at², we get

100 = (1/2) × 0.6 × t²

or t = 18.3 s.