At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Tsunamis are dangerous! Scientists use the formula [tex]\( s = \sqrt{9.8 d} \)[/tex] to calculate the speed [tex]\( s \)[/tex] of the tsunami (in meters per second) based on the depth [tex]\( d \)[/tex] of the ocean (in meters).

What is the depth of the ocean (to the nearest meter) if the tsunami is moving at a speed of 320 meters per second?


Sagot :

Sure! Let's find the depth of the ocean when the tsunami is moving at a speed of 320 meters per second, using the given formula [tex]\( s = \sqrt{9.8 d} \)[/tex].

Step-by-Step Solution:

1. Given Parameters:
- Speed of the tsunami [tex]\( s = 320 \)[/tex] meters per second
- Acceleration due to gravity [tex]\( g = 9.8 \)[/tex] meters per second squared

2. Formula:
The relationship between the speed [tex]\( s \)[/tex] and the depth [tex]\( d \)[/tex] is given by:
[tex]\[ s = \sqrt{9.8 d} \][/tex]

3. Rearrange the Formula to Solve for Depth [tex]\( d \)[/tex]:
[tex]\[ s = \sqrt{9.8 d} \][/tex]
First, square both sides to eliminate the square root:
[tex]\[ s^2 = 9.8 d \][/tex]
Now, solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{s^2}{9.8} \][/tex]

4. Substitute the Given Values:
- [tex]\( s = 320 \)[/tex] meters per second
[tex]\[ d = \frac{320^2}{9.8} \][/tex]

5. Calculate the Depth [tex]\( d \)[/tex]:
[tex]\[ d = \frac{102400}{9.8} \approx 10448.979591836734 \][/tex]

6. Round to the Nearest Meter:
The depth [tex]\( d \)[/tex] rounded to the nearest meter is:
[tex]\[ d \approx 10449 \][/tex]

Conclusion:
The depth of the ocean is approximately 10,449 meters if the tsunami is moving at a speed of 320 meters per second.