Question

a tsunami is a destructive, fast - moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. the pacific tsunami warning center is responsible for monitoring earthquakes that could potentially cause tsunamis in the pacific ocean. through measuring the water level and calculating the speed of a tsunami, scientists can predict the arrival times of tsunamis.
the speed, s (in meters per second) at which a tsunami moves is determined by the depth, d (in meters) of the ocean. ( s=sqrt{gd} ), where g is approximately 12.5 meters per second squared.
find the depth of a tsunami in a region of the ocean that is moving at the average speed of 86 meters per second.
round your answer to the nearest meter. do not include units in your answer.
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Explanation:

Step1: Substitute the values into the formula

Given \(s = 86\) and \(g=12.5\), substitute into \(s=\sqrt{gd}\). So, \(86=\sqrt{12.5d}\).

Step2: Square both sides of the equation

Squaring both sides gives \(86^{2}=(\sqrt{12.5d})^{2}\). Since \((\sqrt{x})^{2}=x\), we have \(7396 = 12.5d\).

Step3: Solve for \(d\)

Divide both sides by \(12.5\): \(d=\frac{7396}{12.5}\).

Step4: Calculate the value of \(d\)

\(\frac{7396}{12.5}=591.68\).

Step5: Round to the nearest meter

Rounding \(591.68\) to the nearest meter gives \(592\).

Answer:

\(592\)