Home
Class 12
PHYSICS
A swimmer starts to swim from point a to...

A swimmer starts to swim from point a to cross a river. He wants to reach point B on the opposite side of the river. The line AB makes an angle `60^(@)` with the river flow as shown. The velocity of the swimmer in still water is same as that of the water
(i) In what direction should he try to direct his velocity ? Calculate angle between his velocity ? Calculate angle between his velocity and river velocity.
(ii) Find the ratio of the time taken to cross the river in this situation to the minimum time in which he can cross this river.

Text Solution

Verified by Experts

The correct Answer is:
(i) `120^(@)` (ii) `2//sqrt3`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A swimmer starts to swim from point a to cross a river. He wants to reach point B on the opposite side of the river. The line AB makes an angle 60^(@) with the river flow as hown. The velocity of the swimmer in still water is same as that of the water (i) In what direction should he try to direct his velocity ? Calculate angle between his velocity anf river velocity. (ii) Find the ratio of the time taken to cross the river in this situation to the minimum time in which he can cross this river.

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30^(@) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle theta with the line AB should be _________ ""^(@) , so that the swimmer reaches point B.

Knowledge Check

  • A swimmer crosses the river along the line making an angle of 45^(@) with the direction of flow. Velocity of the river is 5 m/s. Swimmer takes 6 seconds to cross the river of width 60 m. The velocity of the swimmer with respect to water will be :

    A
    `10m//s`
    B
    12m/s
    C
    `5sqrt(5)m//s`
    D
    `10sqrt(2)m//s`

  • A swimmer crosses the river along the line making an angle of 45^@ with the direction of flow. Velocity of the river water is 5(m)/(s) . Swimmer takes 12 seconds to cross the river of width 60 m. The velocity of the swimmer with respect to water will be:

    A
    `10(m)/(s)`
    B
    `5(m)/(s)`
    C
    `5sqrt5(m)/(s)`
    D
    `5sqrt2(m)/(s)`

  • A swimmer wishes to cross a river 500m width flowing at a rate u. his speed w.r.t. still water is v. for this he makes an angle theta with the vertical as shown in the given figure then:

    A
    to cross the river in minimum time `theta=0^(@)`
    B
    to cross the river in minumum time, `theta=30^(@)`
    C
    for u=3km/hr and v=5km/hr, the time taken to cross the river in minimum time will be 6min.
    D
    for u=3 km/hr and v=5km/hr, the time taken to cross the river in minimum time will be 3min.

    • Similar Questions

    Explore conceptually related problems

    A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point B? In which direction should he swim?

    A man wants to reach point B on the opposite bank of a river flowing at a speed u as shown in (Fig. 5.193). What minimum speed relative to water to water should the man have so that he can reach directly to point B ? In which direction should he swim ? .

    A man wants to reach point B on the opposite bank of a river flowing at a speed 4m/s as shown in the fig 1E.125 (a) what minimum speed relative to water should the man have so that he can reach point B directly by swimming? In which direction should he swin?

    A boatman wants to reach from one bank of a 2km wide river to a point on another bank , directly opposite to the point from where he started . If he rows with a speed of 8 km/h , in still water and river flows at the rate of 14km//he , in which direction he should row ?

    Show that the direction of the shortest route is at right angles to the river when the velocity of the swimmer is greater than that of the river. Show also that when the velocity of the swimmer is less than that of the river, the direction is tan^(-1)v//sqrt(u^(2)-v^(2)) where v= velocity of swimmer and u= velocity of river.

    Home
    Profile