A boat which has a speed of 5km/hr in still water crosses a river of width 1km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is ?

the velocity of the river is 3 km /h

please explain how idont want the answer but how the answer comes?

let the velocity of the river be x. the velocity of the river will be in the horizontal direction

velocity of boat in still water is 5km/hr. As the width of the river is 1 km and time taken by the boat to cross the river along the shortest path is 15 min therefore the velocity of the boat is=  1*60/15= 4km/hr

 according to the figure the velocity of the river is along  AB . By applying triangle law of vector addition the value of AB comes to be 3km/hr

Approved

As the boat crosses the river it experiences two forces one horizontal direction (by the river along AX) and another by the one who rows the boat (in the vertical ditection along AB) X A ------ v=3m/s

The width of the river=1.0kmThe boat crosses the river in 15 minutes The resultant velocity of boat =1.0km/0.25h=4km/hVelocity of river=(5²-4²)½ =3km/h

Given - v=5km/hr S=1km t=15/60 hr. From second eq . Of motion 1=1/2×a×(15/60)^2a=8m/s^2From first eq . Of motion5= u+8×15/60 Hence u=3km/hr