Question

A river stream is flowing at 5 km/h. A man wants to reach point B starting from point A as shown in figure. Choose possible values of swimming speed of man in still water to reach directly at point B? B 30: → 5 km/h A​

Answer 1

Given info : A river stream is flowing at 5 km/h. A man wants to reach point B starting from point A as shown in figure.

To find : the speed of man in still water to reach directly at point B is..

solution : let the speed of man in still water to reach directly at point B is v. and the angle made by it with width of river is Ф.

so, vertical velocity of the man, $v_y=vcos\Phi$

horizontal velocity of the man, $v_x=u-vsin\Phi$ , where u is velocity of river stream

now, tan30° = $\frac{v_y}{v_x}$ = $\frac{vcos\Phi}{u-vsin\Phi}$

⇒ $\frac{1}{\sqrt{3}}=\frac{vcos\Phi}{u-vsin\Phi}$

⇒ u - vsinФ = √3vcosФ

⇒ v(sinФ + √3cosФ) = u

⇒ v = $\frac{u}{sin\Phi+\sqrt{3}cos\Phi}=\frac{u}{2sin\left(\frac{\pi}{3}+\Phi\right)}$

if we put the value of Ф = 0° [ means velocity of man doesn't inclined to width of river , he just want to cross the river perpenducularly to the velocity of the stream ]

so, v = 5/2(√3/2) = 2.9 km/h.

so the correct choice is option (c) 2.9 km/h