Real World Problems

Question

In a tsunami, the wave speeds (in meters per second) can be modeled by s(d)=√9.8d, where d is the depth (in meters) of the water. Estimate the depth of the water when the wave speed is 200 meters per second. Round your answer to the nearest whole meter.

The depth of the water is about ? meters

Answer 1

Hi Jordan,

The equation you've written down allows us to find a speed (s) if depth (d) is given, or vice versa.

In this case, we are given speed, s=200m/s and want to find depth.

s(d)=√9.8d

Plug in the given value for s, and solve for d.

That is,

200=√9.8d

How do we get d by itself to solve for it?

Is d under the square root in your equation? (I can't tell, based on how you've written it)

If so, you need to square both sides...

200²=9.8*d

Now, divide both sides by 9.8, because, remember, we want to isolate d...

(200)²/(9.8)=d

I got d=4,081.632 m (check this for yourself!)

Now, it says to round to the nearest whole meter, so you need to round this final answer (:

Answer 2

200 = sqrt( 9.8 d)

40000 = 9.8 d

40000/9.8 = d

d = 4082