Tsunamis are dangerous! Scientists use the formula $$ s=\sqrt{9.8 d} $$ to calculate the speed ( $$ s $$ ) of the tsunami (in meters per second ) based on the depth (d) of the ocean (in meters). The 9.8 refers to the acceleration of the tsunami due to gravity, in meters per second squared. What is the depth of the ocean (to the nearest meter) if the tsunami is moving at a speed of 320 meters per second?

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The depth of the ocean is approximately 10408 meters. To find the depth of the ocean $$ d $$ when the speed of the tsunami $$ s $$ is 320 meters per second, we can use the formula: $$ s = \sqrt{9.8 d} $$ First, we substitute $$ s = 320 $$ into the equation: $$ 320 = \sqrt{9.8 d} $$ Next, we square both sides to eliminate the square root: $$ 320^2 = 9.8 d $$ Calculating $$ 320^2 $$: $$ 320^2 = 102400 $$ Now we have: $$ 102400 = 9.8 d $$ To solve for $$ d $$, we divide both sides by 9.8: $$ d = \frac{102400}{9.8} $$ Calculating the right side: $$ d \approx 10408.16327 $$ Rounding to the nearest meter, we find: $$ d \approx 10408 $$ Thus, the depth of the ocean is approximately **10408 meters**.

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