A man can swim in still water ast a speed of 3 km/h. He wants to cross a river that flows at 2 km/h and reach the point directly oposite to his starting point. A. In which diretionshoeld he try to swim (that is, find the angle his body makes wilth the river flow)? b. How much time will he take to cross the river if the river is 500 m wide?

Explanation

a. The situationis shown in ure. The X-axis is chosen along the river flow and the orign at the starting positionn of the man. The direction of the velocity of man with respect to ground is along the Y-axis (perpendicular to the river). We hasve to find the direction of velocity of the river with respect to the
Let `vecv_(r,g)=`veocity of the river respect to the ground
`=2km/h along the X-axis
`vecv_(m,r)=` velocity of the man with respect to the river `=3 km/h` making an angle `theta` withe the Y-axis and `vecv_(m,g)=` velocity of the man with respect to teh ground along the Y-axis.
We have
`vecv_(m,g)=vecv_(m,r)+vecv_(r,g)` .............i.
Taking component along the X-axis
`0=- (3 km/h)costheta+0`
`or, v_(m,g)=sqrt5 km/h`
`Time = (Displacement in y direction)/(velocity in y direction)
`=(0.5 km)/(sqrt5 km/h)=(sqrt5)/10 h`.