A tsunami (or tidal wave) is a fast-moving ocean wave caused by an underwater ea

Question

A tsunami (or tidal wave) is a fast-moving ocean wave caused by an underwater earthquake. The water first goes down from its normal level and then rises an equal distance above its normal level and finally returns to its normal level over the course of 15 minutes Suppose that a tsunami with an amplitude of 10 meters approaches the pier at Honolulu where the normal depth of the water is 9 meters. Copy from here as needed. a. Find an equation for the depth of the water. Assume that at t 0 the water is at its normal depth and the tsunami is about to hit. th b. What is the minimum depth of the water? at does this mean? c. Use your equation to predict the height of the water at t 2. Round to 3 decimal places. d. Give the two times when the water level will be 15 meters. Round to 3 decimal places and give the smaller answer first. minutes and minutes Check Don't forget to do some problems from the target Target #6 4:46 -GB

Explanation / Answer

comparing with y=Asin(Bt) +D

a)

period,2/B= 15

=>B=(2/15) minutes

minimum =9-10=-1

maximum =9+10=19

mid line, D=9

y=-10sin((2/15)t) +9

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b) minimum depth of water =-1

after depth reaches zero ,the ground can be seen.(there will not be trace of water).

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c)

when t =2

y=-10sin((2/15)*2) +9

y=1.569

height of water is 1.569 meters

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d)

when water level is 15meters, y=15

-10sin((2/15)t) +9=15

=>-10sin((2/15)t) =6

=>sin((2/15)t) =-(3/5)

=>t=9.036minutes and 13.464 minutes

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