How Does Skier Speed Affect Wave Frequency and Wavelength?

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The discussion centers on a physics problem involving a water-skier's speed and its effect on wave frequency and wavelength. The skier moves at 12.5 m/s and experiences different intervals between wave crests depending on her direction relative to the wave. The key equations involve the relationship between wave speed, wavelength, and period. A participant highlights that the skier's speed influences the perceived wavelength but is not directly related to the wave's actual speed. The conversation emphasizes understanding the apparent wavelength from the skier's perspective to solve for the wave's speed and wavelength.
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I am trying to work through this problem to no avail.

Homework Statement



A water-skier is moving at a speed of 12.5 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.498 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.305 s in response to the crests. The speed of the skier is greater than the speed of the wave. Determine (a) the speed and (b) the wavelength of the wave.


Homework Equations



we know that v = wavelength/ period

and that wavelength equals V/f




The Attempt at a Solution



I am having trouble deriving period from the given data. I know that the speed of the wave is propotional to the speed of the water skier, but I am not sure about the correct ratio to use.

any help is appreciated.

-Matt
 
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The speed of the wave has nothing to do with the speed of the water skier. The rate at which the skier hits the wave peaks is related to both the speed of the skier and the wave speed. What is the apparent wavelength of the water wave from the skier's point of view ("reference frame") in each direction? And how can you use those wavelengths to get you your answers?
 

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