A river is flowing from west to east with a speed of 5 m / min. A man can swim in still water with a velocity 10 m / min. In which direction should the man swim so, as to take the shortest possible path to go to the south ?

Question

A river is flowing from west to east with a speed of 5 m / min. A man can swim in still water with a velocity 10 m / min. In which direction should the man swim so, as to take the shortest possible path to go to the south ? (A) 30° east of south (B) 60° east of south (C) 60° west of south (D) 30° west of north

Tardigrade Admin · Accepted Answer

Let the swimmer swims at an angle θ with the vertical. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c3bec47db59b515d22f63007d04fa63b-.png" /> ∴ sin θ =(vr/vs)=(5/10)=(1/2)= sin 30° θ =30° The swimmer should swim 30° east of south to take the shortest possible path to go to the south.

Q. A river is flowing from west to east with a speed of $5 m / min$ . A man can swim in still water with a velocity $10 m / min$ . In which direction should the man swim so, as to take the shortest possible path to go to the south ?

$3 0^{\circ}$ east of south

$6 0^{\circ}$ east of south

$6 0^{\circ}$ west of south

$3 0^{\circ}$ west of north

Let the swimmer swims at an angle $θ$ with the vertical.

$∴ sin θ = \frac{v _{r}}{v _{s}} = \frac{5}{10} = \frac{1}{2} = sin 3 0^{\circ}$
$θ = 3 0^{\circ}$
The swimmer should swim $3 0^{\circ}$ east of south to take the shortest possible path to go to the south.

Q. A river is flowing from west to east with a speed of 5m/min. A man can swim in still water with a velocity 10m/min. In which direction should the man swim so, as to take the shortest possible path to go to the south ?

30∘ east of south

60∘ east of south

60∘ west of south

30∘ west of north