Question

A water-skier is moving at a speed of 16.7 m/s. When she skis in the same direction as a traveling wave, she springs upward every 6.9 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 4.2 s in response to the crests. The speed of the skier is greater than the speed of the wave.
Determine the speed of the wave in m/s and Determine the wavelength of the wave.

Answer 1

λ=(v-u) ∙t₁
λ=(v+u) ∙t₂
(v-u) ∙t₁=(v+u) ∙t₂
u=v(t₁-t₂)/(t₁+t₂) =16.7(6.9-4.2)/(6.9+4.2)=
=16.7∙2.7/11.1=4.06 ㎧
λ=(v+u) ∙t₂=(16.7+4.06) ∙4.2=87.2 m.