First slide

Newton's laws of motion

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 where as
the mass of second boat is double of this mass. If the initial distance between the boats was 120 m, the time taken for two boats to meet each other is (neglect water resistance between boats and water)

Moderate

A

15 s
B

20 s
C

5 s
D

30 s

Solution

The force of 100 N acts on both the boats.
$\begin{array}{l} 250 a_{1} = 100 and 500 a_{2} = 100 \\ or a_{1} = 0.4 {ms}^{- 2} and a_{2} = 0.2 {ms}^{- 2} \end{array}$
The relative acceleration: $a = a_{1} + a_{2} = 0.6 {ms}^{- 2}$
$Using S=ut+ \frac{1}{2} a t^{2}, we get$
$120 = (1 / 2) \times 0.6 \times t^{2} or t = 20 s$

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