Home
Class 12
PHYSICS
A man swims across a river with speed of...

A man swims across a river with speed of `V_(m)` perpendicular to the flow direction of river. If the water flows with a speed ` V_(w)` with what resullant velocity does the man cross the river ?

Text Solution

Verified by Experts

The directions of `barv_(m)` and `barv_(w)` are shown in the figure. Using the triangle method the resultant velocity is given by third side of `DeltaAOC` taken in opposite order .

`bar(AC)=bar(AO)+bar(OC)`
` |bar(AC)|=sqrt(A0O^(2)+OC^(2))" " ` [ Using Pythagoras theorem ]
`= sqrt(v_(m)^(2)+v_(w)^(2))`
The direction `theta ` that the resultant makes with the `barv_(m)` is
`tan theta =(|barv_(w)|)/(|barv_(m)|)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A man swims across a river with speed of 5 km h^(-1) ( in still water). While a boat goes upstream with speed 12 km h^(-1) ( in still water). How fast and in which direction does, the man appear to go to the boatman ? Given that the speed of flowing water is 2 km h^(-1)

A man swim at an angle theta=120^(@) to the direction of water flow with a speed V_(mw) =5 km/hr relative to water.If the speed of water V_(w) =3 km/hr, Find the speed of the man.

A man who can swim at a velocity v relative to water wants to cross a river of width b, flowing with a speed u.

A man who can swim at a velocity v relative to water wants to cross a river of width b, flowing with a speed u.

A boat 'B' is moving upstream with velocity 3m//s with respect to ground. An observer standing on the boat observes that a swimmer 'S' is crossing the river perpendicular to the direction of motion of the boat. If river flow velocity is 4m//s and swimmer crosses the river of width 100,m is 50s . Then

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?

The width of a river is 3 sqrt(3) km. A boat has a velocity of sqrt(3) km/s and starts to cross the river in a direction perpendicular to the bank of the river. If the river is flowing with a velocity 2km/sec, find the distance drifted by the boat.

The stream of a river is flowing with a speed of 2km//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 ot cross the river straight ?

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, and the width of the river is 2 km, the time taken to cross the river is (in hours)

A man desires to swim across the river in shortest time. The velcoity of river water is 3 km h^(-1) . He can swim in still water at 6 km h^(-1) . At what angle with the velocity of flow of the river should he swim ?