A water-skier is moving at a speed of 12.9 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.805 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.683 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.

λ= 11.84 , V= 1.06m/s

Explanation:

Speed of skiesr= 12.9m/s

Distance between each Crest is wavelength (λ)

When skier moves in same direction

Relative Velocity= 12.9 -V

(12.9-V)(0.805)= λ (1)

When in the opposite direction

(12.9+V)(0.683)= λ (2)

From equ 1 and 2

(12.9-V)(0.805) = (12.9+V)(0.683)

10.3845-0.805V= 8.8107+ 0.683V

10.3845-8.8107= 0.683v - 0.805v

1.5738 = 1.488v

V= 1.06m/s

From Equ 1

12.9 - V = λ

12.9 - 1.06= 11.84

λ= 11.84

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