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.

Velocity of a swimmer with respect to a river is (hat i+4hat j)m/s and velocity of the river flow is (2hat j)m/s then velocity of swimmer with respect to ground is (in m/s)

A man wishes to cross a river flowing with velocity u swims at an angle theta with the river flow.If the man swims with speed v and if the width of the river is d , then the drift travelled by him is

Two swimmers leave point A on one bank of the river to reach point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and them walks the distance that he has been carried by the stream to get to point B . what was the velocity v_(0) of his walking if both swimmers reach the destination simultaneously? The stream velocity is u and v is the velocity of swimmer in still water.

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.

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

Two swimmers leave point A on the bank of the river to reach point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get to point B. What was the velocity u of his walking if both swimmers reached the destination simultaneously? The stream velocity v_0=2.0 km//hour and the velocity v^' of each swimmer with respect to water equals to 2.5km per hour.

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 boat moves relative to water with a velocity v which is n times less than the river flow velocity u . At what angle to the stream direction must the boat move to minimize drifting ?