Question

A man is trying to cross a river to cross a river flowing at a speed of $5m{s}^{-1}$ to least possible displacements by swimming at an angle of 143 to the stream. The drift he suffers when he is crossing the same river in least possible time is (Width of river = 1 km)

• A. 160 m
• B. 800 m
• C. 400 m
• D. 200 m

Answer 1

The correct option is B 800 m

let river velocity is $\overrightarrow{v_r}=5\hat{i}$

A man is trying to cross a river least possible displacements by swimming at an angle of 143 to the stream

Let the velocity of the man is $v_m$

shown in the diagram $v_{m}sin{53}^0=5$

$\Rightarrow v_m=\frac{25}{4}$

The drift he suffers when he is crossing the same river in the least possible time is D when he cross the river perpendicular to the direction of the river flow , time taken by the man is t

$\Rightarrow t=\frac{S}{v}=\frac{1000}{25}\times 4=160sec.$

drift is $D=v_{r}t=5\times 160=800m$