The speed that a tsunami can travel is modeled by the equation [tex]\( S = 358 \sqrt{d} \)[/tex], where [tex]\( S \)[/tex] is the speed in kilometers per hour and [tex]\( d \)[/tex] is the average depth of the water in kilometers.

What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

A. 0.32 km
B. 0.75 km
C. 1.12 km
D. 3.17 km



Answer :

To determine the approximate depth of water for a tsunami traveling at 200 kilometers per hour, we can use the equation provided:

[tex]\[ S = 358 \sqrt{d} \][/tex]

where [tex]\( S \)[/tex] is the speed in kilometers per hour and [tex]\( d \)[/tex] is the average depth of the water in kilometers.

Here are the steps to solve for [tex]\( d \)[/tex]:

1. Substitute the given speed [tex]\( S = 200 \)[/tex] km/h into the equation:

[tex]\[ 200 = 358 \sqrt{d} \][/tex]

2. Isolate the square root term by dividing both sides of the equation by 358:

[tex]\[ \sqrt{d} = \frac{200}{358} \][/tex]

3. Calculate the intermediate result:

[tex]\[ \frac{200}{358} \approx 0.5587 \][/tex]

4. Square both sides to solve for [tex]\( d \)[/tex]:

[tex]\[ d = (0.5587)^2 \][/tex]

5. Calculate the depth [tex]\( d \)[/tex]:

[tex]\[ d \approx 0.3121 \, \text{km} \][/tex]

Thus, the approximate depth of the water for a tsunami traveling at 200 kilometers per hour is:

[tex]\[ \boxed{0.32 \, \text{km}} \][/tex]