CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Crossing the River(Minimum Time)

2 km wide riv...

Question

$2 k m$ wide river flowing at the rate $5 k m / h r$ . A man can swim is still water $10 k m / h r$ . He wants to cross the river along the shorted path. Find-
(a) in which direction should the person swim.
(b) crossing time.

Open in App

Solution

Since the man goes along the shortest path.
So, $10 cos θ = 5$
$cos θ = \frac{1}{2}$
$θ = 60^{o}$ from opposite to flow
or $θ = 180 - 60$ from flow
$= 120^{o}$
Time taken $= \frac{d i s t a n c e}{s p e e d} = \frac{2}{10 sin 60}$
$= \frac{1}{5 \times \frac{\sqrt{3}}{2}}$
$= \frac{2}{5 \sqrt{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

5 km

wide is flowing at the rate of

2 km/hr

. The minimum time taken by a boat to cross the river with a speed

5 km/hr

(in still water) is approximately

Q. A man can swim in still water at a speed of

3 k m / h

. He wants to cross a river that flows at

2 k m / h

and reach the point directly opposite to his starting point.
(a) In which direction should he try to swim (that is, find the angle his body makes with the river flow)?
(b) How much time will he take to cross the river if the river is

500 m

Q. A man can swim in still water with a speed of

2 m s^{- 1}

. If he wants to cross a river of water current speed

\sqrt{3} m s^{- 1}

along shortest possible path, then in which direction should he swim?

Q. A man who can swim at the rate of

2 k m / h r

(in still river) cross a river to a point exactly opposite on the other bank by swimming in a direction of

120^{o}

to the flow of the water in the river. The velocity of the water current in

k m / h

Q. A man can swim at a speed of

3 k m h^{- 1}

in still water, he wants to cross a

500 m

wide river flowing at

2 k m h^{- 1}

. He keeps himself always at an angle of

120^{o}

with the river flow while swimming
Choose the correct options

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Vector Components

PHYSICS

Watch in App

explore_more_icon

Explore more

Crossing the River(Minimum Time)

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon