Final answer:
To find the water depth for a tsunami wave speed of 200 m/s using the model s(d) = √(9.8d), square the speed and divide by 9.8. The estimated depth is approximately 4081.63 meters.
Step-by-step explanation:
To find the depth of water when the wave speed is 200 meters per second using the tsunami wave model s(d) = √(9.8d), we need to solve for d in the equation s(d) = 200. In this equation, s represents the speed of the wave in meters per second, and d represents the depth of the water in meters.
Let's set up the equation with the given wave speed:
200 = √(9.8d)
To solve for d, we first square both sides of the equation to get rid of the square root:
200² = (√(9.8d))²
40000 = 9.8d
Next, we divide both sides by 9.8 to isolate d:
d = 40000 / 9.8
d ≈ 4081.63
Thus, the estimated depth of water where the tsunami wave speed is 200 meters per second is approximately 4081.63 meters.