1. ## swimmer crossing river

a girl wants to swim across a river 50 m wide. the river flows with a velocity of u m s-1 parallel to the banks. the girl swims at a velocity v m s^-1 . she crosses the river as quick as possible and she takes 75 seconds and she is carried down stream by 30 m. find (i) u and v (ii) how long it will take her to swim back in a straight line to her original position.

for (i) i know she heads straight across cross the river in the shortest time. to find her j direction speed which is v i ca use distance/time so v= 50/75=2/3 m s^-1

its the same for the river current so u= 30/75 =2/5m s^-1

i am not sure how to do part (ii)

2. ## Re: swimmer crossing river

here is a pic for (ii), sorry it is bad.

i think it can be solved using the sine /cosine rule. i am able to calculate a in the diagram and also 1 of the angles in the vector triangle.
it can also be solved using relative velocity and the formula Vgr=Vg-Vr

3. ## Re: swimmer crossing river

She starts at position $(30,50)$ and initially swims to the origin $(0,0)$.

The magnitudes of u and v you calculated are correct.

Let $\theta$ be the angle she swims relative to the river bank to return to $(30,50)$. Using components ...
$\dfrac{2}{3} \cdot t \cos{\theta} - \dfrac{2}{5} \cdot t = 30$
$\dfrac{2}{3} \cdot t \sin{\theta} = 50$
Solving the system for $t$, I calculate it will take about 159 seconds for her to swim back to her starting position.