# A man crosses the river in shortest time at an angle $\theta=60 ^{\circ}$ to the direction of flow of water. If the speed of water is $v_w=4\; km/hr$ find the speed of man.

$(a)\;6km/hr \quad (b)\;10km/hr \quad (c)\;12km/hr \quad (d)\;8 km/hr$

Let $\overrightarrow {v_m}$be the velocity of man
we know that to cross river in minimum time the man should head $\perp$ to the direction of river.
$\overrightarrow {v_m} \perp \overrightarrow {v_w}$
Therefore $\cos \theta=\Large\frac{v_w}{v_m}$
$=>\cos 60=\Large\frac{4}{v_ m}$
$=>v_m=\large\frac{4}{\cos 60}$
$=>\large\frac{4}{1/2}$$=8km/hr$
edited May 23, 2014