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Rain is falling at the speed of 4 km/hr from west direction making an angle $30^{\circ}$ with vertical. At what speed should a man walk eastward, such that he has to hold his umbrella vertically to protect himself

\[(a)\;6.518 km/hr\quad (b)\;2 km/hr \quad (c)\;3.464 km/hr \quad (d)4.236 km/hr\]

1 Answer

Relative velocity of rain w.r.t. man must be vertical.
=> the resultant of $v_{\large rain}$ and $(-v_{\large man})$ must be vertical.
$\large\frac{v_{\Large m}}{v_{{\Large rain}}}=$$\sin 30^{\circ}$$=\large\frac{1}{2}$
Hence b is the correct answer.
answered Jun 27, 2013 by meena.p
edited May 23, 2014 by lmohan717

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