1. relative velocity

a girl can swim at u ms^-1 in still water. she swims across a river of width d metres. the river flows with a constant speed of v ms^-1 . parallel to the straight banks. where v<u. crossing the river by the shortest path the girl takes 12 seconds. find in terms of v and u the time it takes in terms of v and u the woman takes.

do i have my labels of vg,vr and vgr right?

i know vgr=vg-vr

vg stand for the vector of the girl

vgr stands for the vector girl relative to the river which also represents the actual direction the girl is travelling . am i right when i say this?

2. Re: relative velocity

i know vgr=vg-vr

$v_g + \color{blue}{v_r} = \color{red}{v_{gr}}$

3. Re: relative velocity

yes i am getting confused on that exactly. its like that in my text book but i do understand the labels and i would of thought it is the way i posted it in my diagram.

should vg not represent the actual way the girl is travelling which is straight across? and vgr should represent the way she sets out to go which is upstream

4. Re: relative velocity

Originally Posted by markosheehan
yes i am getting confused on that exactly. its like that in my text book but i do understand the labels and i would of thought it is the way i posted it in my diagram.

should vg not represent the actual way the girl is travelling which is straight across? and vgr should represent the way she sets out to go which is upstream
If the girl directs her velocity in the direction of $v_g$, then the river will push her with a velocity of $v_r$ and her net velocity will be $v_{gr}$, which will take her the shortest path across the river. So, $v_g+v_r = v_{gr}$.

5. Re: relative velocity

sorry never mind i get it now i think

6. Re: relative velocity

Originally Posted by markosheehan
sorry never mind i get it now i think
the "labels" are not that important if you understand the relationship ...

If you wanted to swim directly across a river to a point directly opposite to your starting position, you would have to direct your swim path upstream a bit to counter the current that would take you downstream if you did not make the corrective adjustment.

Airplanes fly between two fixed points on the Earth using the same concept ... the adjustment of the airplane into the wind is called the "crab" angle, greatest when the airplane is flying relative to a direct crosswind.

7. Re: relative velocity

thanks. i do get it now however i find the relationship a bit more confusing when they are crossing a river in the shortest time(they should head straight across) and its even more confusing when they have to be at a point 50 m down the river from where they started( they might have to head slightly up stream which would be vector swimmer relative to the the river which is the vector they would have if the river was not flowing)

i am now not able to solve the question in the OP. the girl j velocity is √(u^2 -v^2) the distance is d. so using d/s*t √(u^2 -v^2)/d =12 for some reason the answer at the back of the book is 12√(u^2 -v^2)/u

8. Re: relative velocity

I don't understand the original problem. It tells you it takes the girl 12 seconds to cross by the shortest route. In terms of u and v, the time it takes her is still 12 seconds.

9. Re: relative velocity

Originally Posted by markosheehan
a girl can swim at u ms^-1 in still water. she swims across a river of width d metres. the river flows with a constant speed of v ms^-1 . parallel to the straight banks. where v<u. crossing the river by the shortest path the girl takes 12 seconds. find in terms of v and u the time it takes in terms of v and u the woman takes.
The last sentence makes little sense ... are the "girl" and the "woman" the same person?

Can you post the original problem, please?

10. Re: relative velocity

Sorry for the delay in the reply. I did post the original problem in the first paragraph of the OP . I think there is something wrong with the question.