Question

The The velocity exceeds 170 meters per second at a depth of about velocity v

(in meters per second) of a tsunami can be modeled by the function v(x)=9.8x−−−−√
, where x
is the water depth (in meters). At what depth does the velocity of the tsunami exceed 170 meters per second? Round your answer to the nearest meter.

Answer 1

The first thing we must do for this case is to rewrite the function.
We have then:
v (x) = root (9.8 * x)
Substituting values we have:
170 = root (9.8 * x)
We clear x:
170 ^ 2 = 9.8 * x
We clear x:
x = (170 ^ 2) / (9.8)
x = 2948.979592 m
Round to the nearest meter:
x = 2949 m
Answer:
The velocity of the tsunami exceed 170 meters per second at:
x = 2949 m