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

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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$

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