A monster storm located 1200 km north of Hawaii generates wind waves with maximum wavelengths of 150 m. Calculate how much time you have to get to the north shore and surf the first big waves. Assume that the average depth of the North Pacific is 3800 m, and that there is no dissipation of wave energy as these waves propagate. Give answer in hours.

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To calculate the time it takes for the waves to reach the north shore, we can use the formula for deep-water wave speed:

v = √(g * λ / (2π))

Where:
v is the wave speed,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
λ is the wavelength of the wave.

First, let's convert the wavelength from meters to kilometers:

λ = 150 m = 0.15 km

Next, substitute the values into the formula:

v = √(9.8 * 0.15 / (2π))

Calculating this equation gives us:

v ≈ 2.462 km/hour

Now that we have the wave speed, we can determine the time it takes for the waves to travel the distance of 1200 km by dividing the distance by the speed:

time = distance / speed = 1200 km / 2.462 km/hour

Calculating this equation gives us:

time ≈ 487.25 hours

Therefore, it would take approximately 487.25 hours for the waves to reach the north shore, assuming no dissipation of wave energy or other factors.