The nature of waves and Periodic waves

[harkkam]

Homework Statement

A water-skier is moving at a speed of 13.3 m/s. When she skis in the same direction as a traveling wave, she springs upward every 6.2 s because of the wave crests. When she skis in the direction opposite to the direction in which the wave moves, she springs upward every 3.5 s in response to the crests. The speed of the skier is greater than the speed of the wave.

Determine Speed of the wave

Determine Wavelength of wave

Homework Equations

v=f*(lamda)
v=d*t
f= 1/t

The Attempt at a Solution

I know that in 6.2 seconds that he is going from crest to crest of a wave. Which means in 6.2 seconds he is completing one cycle. 6.2 seconds is the Period of the wave. His skier moves at 13.3.

That means that the distance he covers is 6.2*13.3 = 82.46m
This 82.46 m is the distance between two crests or equal to one wavelength.

I get stuck here and I get marked wrong by the online HW website. Plz help

 

[Delphi51]

Very tricky business! At least it is motion at constant speed, so we must use
d = vt for the water skier.
In the first case, going from crest to crest, I would say the distance is
λ + 6.2*v, the velocity 13.3 and the time 6.2. Here v is the speed of the wave crests.
If you write another d=vt for the second case, perhaps you can solve the system of two equations for λ and v.

 

[harkkam]

But how did you know that the distance the skier covers is (lamda + 6.2*v) Not just lamda. Why is he going something extra.