Question

if an object is dropped from a height of 116 feet, the function h(t)=-16t^2+116 gives the height of the object after t seconds. when will the object hit the ground? Please EXPLAIN EVERY STEP!!!!!!!!!!!!

Answer 1

Answer:
height = √(29/4) or ~2.69

Quadratic:
h(t) = -16t² + 116
0 = -16t²+ 116 height would be 0 feet when object hits the ground
0 = -4(4t² - 29) find GCF (Great Common Factor)
0 = 4t² - 29 divide each side by GCF
29 = 4t² isolate t
29/4 = t²
√(29/4) = t

Answer 2

To determine the time that the object will hit the ground, you would need to substitute h = 0, since it hits the ground with respect to the building or the height it was dropped from it would be 0.

The time initially is 0, as this is the point that the object is first dropped off from a height of 116 feet.

Solve for t, that will provide the time it takes for the object to hit the ground.

Since the time that the object is dropped is 0, at the top, and the time that the object is on the ground is some value that you calculate.

The duration of time that it takes for the object to hit the ground is the difference between the 2 heights.