Question

The function y = –16t2 + 224 models the height y 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.
(1 point)
Responses

0.25 seconds
0.25 seconds

5.29 seconds
5.29 seconds

7.48 seconds
7.48 seconds

3.74 seconds

Answer 1

To find the time it takes for the stone to hit the ground, we need to find when the height y is equal to 0.

Setting the equation y = -16t^2 + 224 equal to 0, we have:

-16t^2 + 224 = 0

Divide both sides of the equation by -16:

t^2 - 14 = 0

Add 14 to both sides of the equation:

t^2 = 14

Take the square root of both sides of the equation:

t = ±√14

Since time cannot be negative in this context, we only consider the positive solution:

t ≈ √14 ≈ 3.74 seconds

Therefore, it will take the stone approximately 3.74 seconds to hit the ground.