Question

2
select the correct answer
dan uses a remote control to make his drone take off from the ground. function h represents the height, in feet, of the drone t seconds after it begins flying.
h(t) = -16(t - 2)^2 + 64
which statement correctly describes this situation?
a. the drone is on the ground at 2 and 4 seconds.
b. the drone is on the ground at 0 and 16 seconds.
c. the drone is on the ground at 0 and 4 seconds.
d. the drone is on the ground at 0 and 2 seconds.

Explanation:

Step1: Understand the problem

We need to find when the drone is on the ground, which means the height \( h(t) = 0 \). So we set the function \( h(t)=- 16(t - 2)^{2}+64 \) equal to 0 and solve for \( t \).

Step2: Set up the equation

Set \( h(t) = 0 \):
\[
-16(t - 2)^{2}+64=0
\]

Step3: Solve for \( (t - 2)^{2} \)

Subtract 64 from both sides:
\[
-16(t - 2)^{2}=- 64
\]
Divide both sides by - 16:
\[
(t - 2)^{2}=\frac{-64}{-16}=4
\]

Step4: Solve for \( t \)

Take the square root of both sides:
\[
t - 2=\pm\sqrt{4}=\pm2
\]
Case 1: \( t - 2 = 2 \)
\[
t=2 + 2=4
\]
Case 2: \( t - 2=-2 \)
\[
t=-2 + 2=0
\]
So the drone is on the ground at \( t = 0 \) seconds (when it starts) and \( t = 4 \) seconds.

Answer:

C. The drone is on the ground at 0 and 4 seconds.