An earthquake on the ocean floor in the Gulf of Alaska induces a tsunami (sometimes called a "tidal wave") that reaches Hilo, Hawaii, 4380 km away, after a time of 9.55 h. Tsunami’s have enormous wavelengths (100- 200 km), and for such waves the propagation speed is v ≈ q g d , where d is the average depth of the water, d is in meters, v is in m/s, and g = 9.8 m/s 2 . From the information given, find the average ocean depth between Alaska and Hawaii. (This method was used in 1856 to estimate the average depth of the Pacific Ocean long before soundings were made to give a direct determination.) Answer in units of km.

The average ocean depth between Alaska and Hawaii is 1.7 km

Explanation:

First list out the parameters given:

distance (between Alaska & Hawaii) = 4380 km = 4.38 * 10^6 m,

time interval = 9.55 hours = 34380 s, g = 9.8 m/s^2

velocity = distance ÷ time interval

v = x ÷ t = 4380 ÷ 9.55 OR 4.38 * 10^6 ÷ 34380

v = 458.64 km/hr OR 127.4 m/s

From the propagation speed equation given, we make 'd' the subject of the equation. We have:

distance (depth

average depth = velocity ^ 2 ÷ acceleration due to gravity

d = v^2 ÷ g = 127.4 ^ 2 ÷ 9.8

d = 1656.2 m

To convert the average depth from meters to kilometers, divide by 1000

d = 1656.2 ÷ 1000 = 1.6562 km

d = 1.66 km = 1.7 km

Therefore, the average ocean depth between Alaska and Hawaii is about 1.7 km

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