Home
Class 12
PHYSICS
A river is flowing from west to east at ...

A river is flowing from west to east at a speed of ` 5 metres per minute` . A man on the south bank of the river , capable of swimming at `10 metres per minute`, in still water , wants to swim across the river in the shortest time . He should swim in a direction

Text Solution

Verified by Experts

The situation is shown in fig.
OA=A, represents velocity of river which is 5 `mt^(-1)`
OB = B, represents velocity of man in still water which is 10 m `m t^(-1)`
The man starts swimming from 0 and goes along OB tot reach C by shortest possible path.
Hence, `angle AOC = beta = 90^@ `
Here, A= 5 m `m t^(-1) , B = 10m mt^(-1) beta = 90^@ , theta = ?`
From formula,` tan beta = ( B sin theta )/(A+B cos theta )`
Putting values, we get, `tan 90^@ =(10 sin theta )/( 5+10 cos theta ) = oo ` (infinite)
Hence, `5+10 cos theta = 0 `or `10 cos theta =-5`
(or) `cos theta =-0.5 = cos 120^@ i.e., theta = 120^@ `
It makes `angle COB = 30^@ `
The man should swim along OB which is `30^@ ` west of north.
Promotional Banner

Topper's Solved these Questions

  • ELEMENTS OF VECTORS

    AAKASH SERIES|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • ELEMENTS OF VECTORS

    AAKASH SERIES|Exercise SHORT ANSWER TYPE QUESTIONS|10 Videos

  • ELECTROSTATICS

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (PRACTICE SHEET (ADVANCED) INTEGER TYPE QUESTIONS)|5 Videos

  • GEOMETRICAL OPTICS

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II PRACTICE SHEET (ADVANCED) INTEGER TYPE QUESTIONS)|10 Videos

Similar Questions

Explore conceptually related problems

A river is following from west to east at a speed of 5m/minute. A boy on the south bank of the river, capable of swimming at 10 meters/minute in still water, wants to swin across the river in the shortest time, (i) Find the direction in which he should swin, (ii) find the direction when drift along the river is zero.

A river is flowing from west to east at a speed of 5m//s . A man on the south bank of the river capable of swimming at 10m//s in a still water wants to swim, across the river in a shortest time. He should swim in a direction

A river is flowing from east to west at a speed of 5(m)/(min) . A man on south bank of river, capable of swimming (10m)/(min) ini still water, wants to swim across the river in shortest time. He should swim

A river is flowing from the west to the east at 5m/min. A swimmer on the southerm bank can swim at 10 m/min in still water. In what direction should he swim if (i) He wishes to cross the river in minimum time (ii) He wishes to cross te river through shortest route

A swimmer can swim in still water with speed v and the river is flowing with speed v//2 . What is the ratio of the time taken to swimming across the river in shortest time to that of swimming across the river over the shortest distance ?

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 10m//min. In which direction should the man swim so as to take the shortest possible path to go to the south.

2 km wide river flowing with a rate of 5 km/hr. A man can swim in the still water with10 km/hr. He wants to cross the river along shortest path find Crossing time

A river is flowing from west to east with a speed 5 m//s . A swimmer can swim in still water at a speed of 10 m//s . If he wants to start from point A on south bank and reach opposite point B on north bank. In what direction direction should he swim ?

A swimmer can swim in still water with a speed of 2.5 m/s. What is the shortest time taken by him to swim across the river?

A man can swim in still water at a speed of 6 kmph and he has to cross the river and reach just opposite point on the other bank. If the river is flowing at a speed of 3 kmph, he has to swim in the direction