A motor boat is to reach at a point 30^o upstream on the other side of a river flowing with velocity 5 ms^-1. The velocity of motor boat with respect to water is $5 \sqrt{3} {ms}^{- 1}$ . The driver should steer the boat at an angle

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30^o w.r.t. the line of destination from the starting point

120^o w.r.t. stream direction

60^o w.r.t. normal to the bank

None of these

answer is A.

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Detailed Solution

The velocity of motor boat is given as

$\begin{array}{l} {\vec{v}}_{m} = {\vec{v}}_{mw} + {\vec{v}}_{w} \\ \frac{5}{\sin θ} = \frac{5 \sqrt{3}}{\sin 120^{\circ}} \Rightarrow \sin θ = 1 / 2 \Rightarrow θ = 30^{\circ} \end{array}$

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