Question

If an object is dropped from a height of 144 feet, the function h(t)=-16t^2+144 ives the height of the object after t seconds. When will the object hit the ground?\
The choices are:
A. 9 s
B. 6 s
C. 1.5 s
D. 3 s

Answer 1

When the object hits the ground, it is logical to state that its height relative to the ground will be zero (0). Therefore, we'd want to solve for t when h(t) = 0.

h(t) = -16t^2 + 144

-16t^2 + 144 = 0
144 = 16t^2
t^2 = 9
t = 3

Thus the answer would be D. 3 s.

Take note that while the square root of 9 is technically ±3, it is logically impossible to have a negative time value that exists for this function since the object is dropped when t = 0. (You can do the math to check that, when t = 0, h(t) = 144 which is the original height.)

Answer 2

notice that what you have is a parabola equation, the leading coefficient has a negative in front of it, that is, the parabola is going downwards