Question

If speed of water in river is 4 m/ s amd speed of swimmer with respect to water is 3 m/ s then in which direction the swimmer must swim so that he will reach directly opposite end

Answer 1

Given;

Speed of water in river V = 4   $\frac{m}{s}$

Speed of swimmer v = 3  $\frac{m}{s}$

To find;

The direction of swimmer to reach directly opposite end.

Solution;

Let Swimmer is swimming along OB so that he can reach at OC as a resultant.

Let α is the angle between upstream and the swimmer.

and θ is the angle between both ends and the swimmer.

We can see that

θ+α =90°

So

θ = 90° - α

So  Sin θ = Sin( 90° - α )

     Sin θ = Cos  α

Observing figure

Sin θ = Cos  α = $\frac{\textbf{\Large BC}}{\textbf{\Large OB}} = \frac{\textbf{\Large4}}{\textbf{\Large 3}}$

So,   α = $\cos^-^1 \frac{ \textbf{\Large 4}}{ \textbf{\Large 3}}$

As in   $\cos^-^1 (X)$ ,   X =can not be more than 1.

So,  value of α  is not possible. Swimmer can't reach at another end with

3  $\frac{m}{s}$    speed.