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.
