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## Homework Statement

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

swimmers return to the starting point. Which swimmer returns first?

(Note: First guess the answer.)

## Homework Equations

relative velocity and vector

## 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 / [tex]\sqrt{}[/tex]c[tex]^{}2[/tex]+v[tex]^{}2[/tex]

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

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