To determine how many seconds it will take for the phone to hit the ground when dropped from a height of 3,600 feet, we start with the given height equation:
[tex]\[ h(t) = -16t^2 + \text{initial height} \][/tex]
Here:
- [tex]\( h(t) \)[/tex] is the height of the phone at time [tex]\( t \)[/tex] in seconds.
- The initial height is 3,600 feet.
- The phone hits the ground when [tex]\( h(t) = 0 \)[/tex].
Let's set up the equation with these values:
[tex]\[
0 = -16t^2 + 3600
\][/tex]
Now, we need to solve this equation for [tex]\( t \)[/tex].
1. Move the constant term to the other side of the equation:
[tex]\[
16t^2 = 3600
\][/tex]
2. Divide both sides by 16 to isolate [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = \frac{3600}{16}
\][/tex]
3. Simplifying the fraction:
[tex]\[
t^2 = 225
\][/tex]
4. Take the square root of both sides to solve for [tex]\( t \)[/tex]:
[tex]\[
t = \sqrt{225}
\][/tex]
5. Taking the square root of 225 gives:
[tex]\[
t = 15
\][/tex]
Thus, it will take the phone 15 seconds to hit the ground. The intermediate values confirm this result:
- Intermediate calculation for [tex]\( \frac{3600}{16} \)[/tex] gives 225.
- Taking the square root of 225 results in 15.
So, the phone will hit the ground in:
[tex]\[ 15 \text{ seconds} \][/tex]
