A Study in Drowning - Relative motion

Let us take

Velocity of girl in river is Vgs

Velocity of river itself is Vs

Hence, velocity of girl with respect to ground If

She is swimming upstream ( against flow of river ) = Vgs - Vs

She is swimming downstream ( with the flow of river) = Vgs + Vs

Now if she decides to swim across the river

CASE 1 :-

If she wants to cross the river in minimum drift :-

The VcosΘ component should cancel out the opposing stream velocity. This will result in the velocity of girl with respect to the ground to be perpendicular.

CASE 2 :-

If she wants to cross the river in minimum time, her velocity in the river should be perpendicular to the river flow.

Here mimimum time will be = d/ Vmr or d/ Vgs