A swimmer desires to cross a 500 m wide river that is flowing at 5 km/h . His speed relative to the water is 3 km/h . If he heads in a direction making an angle θ with the flow, determine the time he takes to cross the

Correct answer: B. (10)/( θ) minutes Width of the river, d = 500 m = 0.5 km Velocity of the swimmer relative to water, v_ sr = 3 km/h Angle made by the swimmer with the direction of river flow = θ Component of the swimmer's velocity perpendicular to the river flow = v_ sr θ = 3 θ km/h Time taken to cross the river, t = d v_ sr θ t = (0.5)/(3 θ) hours t = (0.5 × 60)/(3 θ) minutes = (10)/( θ) minutes

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

A swimmer desires to cross a 500 m wide river that is flowing at 5...

A swimmer desires to cross a

500 \text{ m}

wide river that is flowing at

5 \text{ km/h}

. His speed relative to the water is

3 \text{ km/h}

. If he heads in a direction making an angle

\theta

with the flow, determine the time he takes to cross the river.

Options

A $\dfrac{10}{\cos\theta} \text{ minutes}$
B $\dfrac{10}{\sin\theta} \text{ minutes}$
C $\dfrac{6}{\sin\theta} \text{ minutes}$
D $\dfrac{6}{\cos\theta} \text{ minutes}$

Correct answer

B. $\dfrac{10}{\sin\theta} \text{ minutes}$

Step-by-step solution

Width of the river,

d = 500 \text{ m} = 0.5 \text{ km}

Velocity of the swimmer relative to water,

v_{sr} = 3 \text{ km/h}

Angle made by the swimmer with the direction of river flow

= \theta

Component of the swimmer's velocity perpendicular to the river flow

= v_{sr} \sin\theta = 3 \sin\theta \text{ km/h}

Time taken to cross the river,

t = \dfrac{d}{v_{sr} \sin\theta}

t = \dfrac{0.5}{3 \sin\theta} \text{ hours}

t = \dfrac{0.5 \times 60}{3 \sin\theta} \text{ minutes} = \dfrac{10}{\sin\theta} \text{ minutes}

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