Question

A man swims across a river with speed of $5km{h}^{-1}$ (in still water), while a boat goes upstream with speed $12km{h}^{-1}$ (in still water). How fast and in which direction does the man appear to go to the boatman? Given that the speed of flowing water is $2km{h}^{-1}$ .

Answer 1

The velocity of boat with respect to river is given as,

$v_b=\sqrt{2^2+{\left(12\right)}^2}$

$v_b=\sqrt{148}m/s$

The relative velocity of man with respect to river is given as,

$v_m=\sqrt{2^2+5^2}$

$v_m=\sqrt{29}m/s$

The direction in which the man appear to go to the boatman is given as,

$\theta ={\cos }^{-1}\left(\frac{v_m}{v_b}\right)$

$\theta ={\cos }^{-1}\left(\sqrt{\frac{29}{148}}\right)$

The speed with which man should move faster is given as,

$V=\sqrt{148-29}$

$V=\sqrt{119}km/hr$