Question

In the middle of math class, Max's pencil rolls off of his desk and onto the ground 2.5 feet below.
Which equation can you use to find how many seconds it takes for the pencil to hit the ground?
If an object falls from s feet above the ground, the object's height in feet, h, after t seconds can be modeled by the formula h=
–
16t2+s.
To the nearest tenth of a second, how long does it take for the pencil to hit the ground?
seconds

Answer 1

To find out how long it takes for the pencil to hit the ground, we can use the given formula:

\[
h = -16t^2 + s
\]

Here, \(h\) represents the height of the pencil above the ground after \(t\) seconds, and \(s\) is the starting height from which the pencil falls.

In your scenario, the pencil starts at a height of \(s = 2.5\) feet, and we want to find out when it hits the ground. When the pencil hits the ground, its height \(h\) will be 0 feet. So we set the equation to 0:

\[
0 = -16t^2 + 2.5
\]

Now, we can solve for \(t\):

1. Rearranging the equation:
\[
16t^2 = 2.5
\]
2. Dividing both sides by 16:
\[
t^2 = \frac{2.5}{16}
\]
3. Taking the square root of both sides:
\[
t = \sqrt{\frac{2.5}{16}} = \sqrt{0.15625}
\]
4. Calculating the square root:
\[
t \approx 0.39 \text{ seconds}
\]

To round to the nearest tenth of a second:
\[
t \approx 0.4 \text{ seconds}
\]

So, it takes approximately **0.4 seconds** for the pencil to hit the ground.