The function f (t) = 16t 2 + 248 models the height f (t) in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.

a. 0.25 seconds

Selected:b. 3.94 secondsThis answer is incorrect.

c. 5.57 seconds

d. 7.87 seconds

Question

Mathematics

London Mckenzie

20 June, 07:41

The function f (t) = 16t 2 + 248 models the height f (t) in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.

a. 0.25 seconds

Selected:b. 3.94 secondsThis answer is incorrect.

c. 5.57 seconds

d. 7.87 seconds

+3

Answers (1)

Know the Answer?

Ellen Garrison · Answer 1

The time it takes for the stone to reach the ground is 3.94 s. This answer is correct.

Step-by-step explanation:

I believe there's a mistake in the equation shown, the acceleration (number that multiplies t²) should be negative, since the stone is falling, therefore I'll answer assuming it's - 16 instead of 16, otherwise there would be no real solution to the equation.

In order to calculate how long it'll take for the stone to hit the ground we must make f (t) = 0 and find the time "t" that makes the equation valid, so we have:

f (t) = - 16t² + 248 = 0

-16t² = - 248

t² = - 248 / (-16) = 15.5

t = sqrt (15.5) = 3.94