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A motor boat is to reach at a point $30^{\circ}$ upstream on the otherside of river flowing with velocity $5m/s$. Velocity of motor boat with respect to water is $5 \sqrt3 m/s$ .The driver should steer the boat at an angle

$\begin{array}{1 1} a)30^{\circ} \text{ with respect to line of destination from starting point.} \\ b)120^{\circ} \text{ with respect to stream direction } \\ c)60 ^{\circ} \text{with respect to normal to back} \\ d)\text{None of these} \end{array}$

1 Answer

Velocity of boat $\overrightarrow v_m=v_{mw}+v_w$
$v_{mw}$= relative velocity of boat with respect to water
$\bar {v} _m =-(5 \sqrt 3 \cos \theta) i+ 5 \sqrt 3 \cos 30 j+5 i$
Taking i direction parallel to river flow and j direction $\perp$ to river flow.
$ \hat v_m=-7.5 i+\large\frac{5 \sqrt 3}{2}$$j+5 \hat i$
$\hat v_m=-2.5 i+\large\frac{5 \sqrt 3}{2}$$j$
$\qquad=\tan^{-1}\bigg[\large\frac{-5 \sqrt 3}{2 \times 2.5}\bigg]$$=\tan ^{-1}(- \sqrt 3)$
answered Jun 27, 2013 by meena.p
edited Jun 27, 2013 by meena.p

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