# Relative Velocity of two swimmers

1. Aug 29, 2007

### JayKo

1. The problem statement, all variables and given/known data

Two swimmers, Alan and Beth, start together at the same point on the
bank of a wide stream that flows with a speed v. Both move at the
same speed c (c > v), relative to the water. Alan swims downstream a
distance L and then upstream the same distance. Beth swims so that her
motion relative to the Earth is perpendicular to the banks of the stream.
She swims the distance L and then back the same distance, so that both

2. Relevant equations

relative velocity and vector

3. The attempt at a solution

let time taken for Alan swim for a distance Ta= L / (V+C)

let time taken for Beth swim for a distance Tb= L / $$\sqrt{}$$c$$^{}2$$+v$$^{}2$$

compare this 2 equation, its obvious Alan will took the less time to finish a distance, L. but the question ask distance of 2L. so i am not sure the vector calculation for Beth to swim back to the origin point.

hope someone can help me out.this is my 1st year physics tutorial question.thanks

Last edited: Aug 29, 2007
2. Aug 29, 2007

### rootX

you forgot to take in account the return distance?
because they returned back to the same place.

it's from Irodov lol

Last edited: Aug 29, 2007
3. Aug 29, 2007

### JayKo

i aware of the return distance which i mention it as 2L.
nonetheless, thank for the tip for Irodov. shall take a look at it carefully.thanks again

4. Aug 30, 2007

### rootX

Ta= L / (V+C) + L / (V-C)
Tb=2*L/$$\sqrt{}$$c$$^{}2$$+v$$^{}2$$

5. Aug 30, 2007

### JayKo

yupe, i got it.thanks :D