Relative Velocity of two swimmers

  • Thread starter JayKo
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  • #1
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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 :eek:
 
Last edited:

Answers and Replies

  • #2
378
2
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 :eek:
you forgot to take in account the return distance?
because they returned back to the same place.

it's from Irodov lol
 
Last edited:
  • #3
128
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you forgot to take in account the return distance?
because they returned back to the same place.

it's from Irodov lol
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
378
2
Ta= L / (V+C) + L / (V-C)
Tb=2*L/[tex]\sqrt{}[/tex]c[tex]^{}2[/tex]+v[tex]^{}2[/tex]
 
  • #5
128
0
Ta= L / (V+C) + L / (V-C)
Tb=2*L/[tex]\sqrt{}[/tex]c[tex]^{}2[/tex]+v[tex]^{}2[/tex]

yupe, i got it.thanks :D
 

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