Question

A swimmer starts swimming in a river (width $=d$) to reach the other end of the river and river velocity is zero when he started the swimming. His velocity is $2.5m/s$ w.r.t. river and once he reaches half of the width of the river, then the river starts flowing with a velocity $2.5m/s$. What is the horizontal displacement of the swimmer from the initial position? ($d=400m$)

• A. $200m$
• B. $100m$
• C. $400m$
• D. $800m$

Answer 1

The correct option is A $200m$

Let the width of the river be ’$d$’ meters.
Swimmer starts swimming with $2.5m/s$ perpendicular to the flow of river.
After reaching halfway, river starts flowing with velocity of $2.5m/s$
Initial velocity of swimmer $=2.5\hat{j}m/s$
After halfway his velocity is $(2.5\hat{i}+2.5\hat{j})m/s$
Let us find out the angle when the river starts flowing
$\tan \theta =\frac{2.5}{2.5}=1$
$\Rightarrow \theta ={45}^{\circ }$
Now distance can be calculated using triangle

$\tan \theta =\frac{x}{d/2}$
$\Rightarrow \tan {45}^{\circ }=\frac{x}{d/2}$
$\Rightarrow 1=\frac{x}{d/2}$
$\Rightarrow x=\frac{d}{2}$
$\therefore x=\frac{d}{2}=200m$