A water-skier is moving at a speed of 14.3 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.450 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.342 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.

a) 1.95 m/s

b) 5.56 m

Explanation:

Given that:

Velocity of the skier = 14.3 m/s

For the skier moving in the direction of the wave, we have:

Period (T) = 0.450 s

Relative velocity (V) of the skier in regard with the wave =  

where:

= velocity of the skier

= velocity of the wave

The wavelength can be written as:

---------------> Equation (1)

For the skier moving opposite in the direction of the wave, we have:

Period (T) = 0.342 s

Relative velocity (V) of the skier in regard with the wave =

The wavelength can be written as:

  ------------------> Equation 2

Equating equation (1) and equation (2) and substituting    = 14.3 m/s ; we have:

Collecting the like terms; we have:

b)

The Wavelength of the wave can be calculated using :  

λ ≅ 5.56 m

answer: 31, 5556. 952 seconds