Determining speed and wavelength of wave
I'm a little stuck on a problem, and would really appreciate some help. The problem is as follows:
A waterskier is moving at a speed of 12.0 m/s. When she skis in the same direction as a travelling wave, she springs upward every 0.600 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 0.500 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.
OK, so here I suppose we are supposed to use the formula:
v = fλ
I figured that when the skier is travelling with the wave, the frequency is: f_1 = 1/T_1 = 1/0.6 = 1.67 Hz
And when the skier is travelling against the wave, the frequency is: f_2 = 1/T_2 = 1/0.5 = 2 Hz
I then assume that we are supposed to have two separate equations such that:
v_1 = 1.67λ
v_2 = 2λ
However, I have a hard time finding a way to express the velocities in the two different scenarios. If anyone can help me along here, I would really appreciate it!
