1. A stationary boat in the ocean is experiencing waves from a storm. The waves

Question

1. A stationary boat in the ocean is experiencing waves from a storm. The waves move at59km/h and have a wavelength of 160m . The boat is at the crest of a wave. How much time elapses until the boat is first at the trough of a wave? Express your answer to two significant figures and include the appropriate units.

2. In the deep ocean, a water wave with wavelength 95 m travels at 12 m/s. Suppose a small boat is at the crest of this wave, 2.0m above the equilibrium position. What will be the vertical position of the boat 3.0s later? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

1)
v = ?f
59km/h * 1m/s / 3.6km/h = 160m * f
f = 0.102 Hz
which means the period is
T = 1/f = 9.76 s
To move from a crest to a trough takes half a period, so the elapsed time is 4.88 s.

2)

You have to use the equation y=A*cos( (2*pi*t) /T)
The crest of the wave is the maximum displacement, so 2 is your amplitude (A).
t is the time, so that is equal to 3.0 s
To find the period, T:
frequency = velocity / wavelength
f = 12/95 = 0.126316 Hz
Period = 1/frequency
T = 1/f = 1/0.126316 = 7.91667

Now you should have everything you need to plug into the equation.
y=2*cos( 2*pi*3.0/7.91667)
y=1.998m <= your answer

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