JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Kinematics

A swimmer wants to cross a river from point A to point B . Line

A B

makes an angle of

3 0^{\circ}

with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle

θ

with the line

A B

should be
____

^{\circ}

, so that the swimmer reaches point B .

Answer: 30

Solution

Let the river speed and the swimmer's speed both be

v

. The river flows at

3 0^{\circ}

to the line

A B

, and the swimmer heads at

θ

A B

on the other side. The swimmer arrives at

B

only if the resultant velocity lies along

A B

, that is if the components perpendicular to

A B

cancel:

v sin θ = v sin 3 0^{\circ}

sin θ = \frac{1}{2}

The swimmer must head at

3 0^{\circ}

to the line

A B

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Integer answer

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