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.
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
1 answer