Optimizing Swimming Across a River: Upstream, Downstream, or Directly Across?

[hafsa786786786]

Homework Statement

If you were trying to swim across a river with the shortest possible time, would you aim your body slightly upstream, directly across the river, or slightly downstream? Explain.

Homework Equations

no equation needed

The Attempt at a Solution

i feel the answer is downstream because you go with the flow of the water and you aren't fighting against the current like you would in the upstream motion.

 

[gneill]

Homework Statement

If you were trying to swim across a river with the shortest possible time, would you aim your body slightly upstream, directly across the river, or slightly downstream? Explain.

Homework Equations

no equation needed

The Attempt at a Solution

i feel the answer is downstream because you go with the flow of the water and you aren't fighting against the current like you would in the upstream motion.

Okay, what might you do to confirm your hypothesis?

 

[AdityaDev]

you can make use of these equations:
$v_b=v_{br}+v_r$
if velocity of river is v_r along +x direction and v_br is thr velocity of boat with respect to river.
the component of v_b along y direction comes out to be dependent only on v_br.Try it.
Now time $t=w/v_{b_y}$ where w is the width of the river.
so you wil have minimum time when v_by is maximum.