Question

A river is flowing with a speed of $1\frac{km}{hr}$. A swimmer wants to go to point 'C' starting from 'A'. He swims with a speed of $5\frac{km}{hr}$, at an angle $\theta$ w.r.t. the river. If AB = BC = 400 m. Then:

• A. The value of $\theta is{53}^{\circ }$
• B. Time taken by the man is 6 min
• C. Time taken by the man is 8 min
• D. The value of $\theta is{45}^{\circ }$

Answer 1

Answer: (A), (B)

Time taken by the man is 6 min


AB = BC = 400 m = 0.4 km
$v_x=5cos\theta +1$
$v_y=5sin\theta$
time taken $\left(t\right)=\frac{AB}{v_y}=\frac{BC}{v_x}$
$\Rightarrow v_y=v_x\Rightarrow 5sin\theta =5cos\theta +1$
$\Rightarrow \theta ={53}^{\circ }$
and $t=\frac{0.4}{5sin\left({53}^{\circ }\right)}=0.1hr=6min.$