Question

A swimmer appears to be moving perpendicular to a man going upstream in a boat. If the velocity of boat w.r.t water is 3 m/s and velocity of river is 1 m/s. Find velocity of swimmer w.r.t ground if it takes 20 seconds for him to cross 60 metre wide river.

• A. $\sqrt{13}m/s$
• B. $8m/s$
• C. $3m/s$
• D. $4m/s$

Answer 1

The correct option is A $\sqrt{13}m/s$

Let the $V_s,V_b\mathrm{and}{V}_r$ be velocities of swimmer, boat and river respectively.
As the swimmer appears to be moving perpendicular to the man inside the boat, the horizontal component of swimmer's velocity will be equal to the velocity of boat
$\Rightarrow V_x=V_b$
We know that $V_{b/r}=3m/s$$\Rightarrow V_b-(-1)=3m/s{V}_b=2m/s$
Thus, $V_x=2m/s$
Similarly $V_y=\frac{d}{t}=\frac{60}{20}=3m/s$
$\therefore$velocity of swimmer be $\sqrt{{V_x}^2+{V_y}^2}$= $\sqrt{13}m/s$