A swimmer crosses a river of width d flowing at velocity V while swimming he heads himself always at an angle of 120° with the river flow and on reaching the other end he find a drift of (d/2) in the direction of flow of river. The speed of the swimmer with respect to river is:

Question

A swimmer crosses a river of width d flowing at velocity V while swimming he heads himself always at an angle of 120° with the river flow and on reaching the other end he find a drift of (d/2) in the direction of flow of river. The speed of the swimmer with respect to river is: (A) (2-√3) V (B) 2(2-√3) V (C) 4(2-√3) V (D) √41

Tardigrade Admin · Accepted Answer

t =( d / V r cos 30) =(2 d /√3 V r ) Now, drift ( d /2) =( V - V r sin 30) t =[ V -( V r /2)][(2 d /√3 V r )] <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/503cefec06c1f74364bcadd5065c21e7-.png" /> √3 Vr=4 V-2 Vr Vr=[(4/2+√3)] V=4(2-√3) V

Q. A swimmer crosses a river of width d flowing at velocity V while swimming he heads himself always at an angle of $12 0^{\circ}$ with the river flow and on reaching the other end he find a drift of $\frac{d}{2}$ in the direction of flow of river. The speed of the swimmer with respect to river is:

$(2 - 3) V$

$2 (2 - 3) V$

$4 (2 - 3) V$

$41$

$t = \frac{d}{V _{r} c o s 30} = \frac{2 d}{3 V _{r}}$
Now, drift $\frac{d}{2} = (V - V_{r} sin 30) t$
$= [V - \frac{V _{r}}{2}] [\frac{2 d}{3 V _{r}}]$

$3 V_{r} = 4 V - 2 V_{r}$
$V_{r} = [\frac{4}{2 + 3}] V = 4 (2 - 3) V$

Q. A swimmer crosses a river of width d flowing at velocity V while swimming he heads himself always at an angle of 120∘ with the river flow and on reaching the other end he find a drift of 2d​ in the direction of flow of river. The speed of the swimmer with respect to river is:

(2−3​)V

2(2−3​)V

4(2−3​)V

41​