If an object is dropped from a height of 200 feet, the function h of t equals negative 16t squared plus 200 gives the height of the object after t seconds. Approximately, when will the object hit the ground?

Question

A. 200.00 seconds
B. 184.00 seconds
C. 3.54 seconds
D. 0.78 seconds

Answer 1

The object will hit the ground when its height is 0. So we need to solve the equation:

-16t^2 + 200 = 0

Dividing both sides by -16, we get:

t^2 - 12.5 = 0

Taking the square root of both sides, we get:

t = ±√12.5

Since time cannot be negative, we only consider the positive root:

t ≈ 3.54 seconds

So the answer is C. 3.54 seconds.