Question

A boy swims in a straight line to reach the other side of a river. His velocity is 5 ms^-1 and the angle of swim with shore is 30^o. Flow of river opposes his movement at 2 ms^-1. If width of river is 200 m, where does he reach the other bank?

• A. 106 m from O' downstream
• B. 186 m from O' downstream
• C. 186 m from O' upstream
• D. 106 m from O' upstream.

Answer 1

Answer: (C)

186 m from O' upstream

Answer 2

Velocity of river ${\overrightarrow{v}}_{r} = - 2\widehat{i}$

Velocity of swimmer w.r.t river is

$\overrightarrow{v}$_s = 5 cos 30$\widehat{i}$ + 5 sin 30$\widehat{j}$

= 4.3$\widehat{i}$ + 2.5$\widehat{j}$

Using $\overrightarrow{v}$_R = $\overrightarrow{v}$_s + $\overrightarrow{v}$_r we get

$\overrightarrow{v}$_R = 2.33$\widehat{i}$ + 2.5$\widehat{j}$

Time taken by swimmer = Distance along y – axis/ y component of velocity

= 200/2.5 = 80 s

Distance moved along x – axis,

O'F = x component of relative velocity × time

= 2.33 × 80 = 186.4 m

~ 186 m upstream