A swimmer can swim in still water at a rate 4.0 km/h. If he swims in a river flowing at 3.0 km/h and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to the ground.

Explanation

The velocityf the swimmer with respect to water is `vecv_(S,R)=4.0 km/h` in the direction respect to the ground is `vecv_(R,G)=3.0 km/h` along the length of the river. The velocity of the swimmer with respect to the ground is `vec_(S,G)` where
`vecv_(S,G)=vecv_(S,R)+vecv_(R,G)`
ure shows the velocities. It is clear that,

`v_(S,G)=sqrt((4.0 km/h)^2+(3.0 km/h)^2)`
`=5.0 km/h`
The angle theta made with the diection of flow is
`tan theta=(4.0 km/h)/(3.0 km/h)=4/3`