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QJEEM21Ph386f: JEE Main 2021 Physics - Class 11 JEEM21Ph386f Solution: A swimmer can swim with velocity of 12 km/h in still water.…

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ____________

^{\circ}

. (Round off to the Nearest Integer) (Find the angle in degrees)

Step-by-Step Verified Solution

The situation is depicted in the following figure.

JEE Main 2021 (Online) 16th March Evening Shift Physics - Motion in a Plane Question 51 English Explanation

where, V_MR = velocity of man = 12 km/h

and v_R = velocity of water flow in river = 6 km/h

As, v_MR should be along CD.

$\Rightarrow v_{R} - v_{M R} \sin θ = 0$

$\Rightarrow 6 - 12 \sin θ = 0 \Rightarrow \sin θ = \frac{6}{12}$

$\Rightarrow \sin θ = \frac{1}{2}$

$\Rightarrow θ = \sin^{- 1} (\frac{1}{2}) = \sin^{- 1} (\sin 30^{\circ})$ [ $∵$ $\sin 30^{\circ} = \frac{1}{2}$ ]

$\Rightarrow θ = 30^{\circ}$

$∴$ $α = 90^{\circ} + θ = 90^{\circ} + 30^{\circ} = 120^{\circ}$

$\Rightarrow α = 120^{\circ}$

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