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]
