For his school's annual egg-drop contest, Nick created a cushioned egg container made of cotton balls and tin foil. In the first round, Nick dropped his egg from the school's second floor balcony 18 feet above the ground, and the egg survived!

Question

Which equation can you use to find how many seconds it took for the egg to hit the ground?
If an object is dropped from s feet above the ground, the object's height in feet, h, t seconds after being dropped can be modeled by the formula h=
–
16t^2+s.

0=
–16t^2+18

18 –16t^2
pick one

To the nearest tenth of a second, how long did it take for the egg to hit the ground?
seconds

Answer 1

To find how many seconds it took for the egg to hit the ground, we can use the given height formula:

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

In this situation, since the egg is dropped from a height of 18 feet, we set \( s = 18 \). Hence, the equation becomes:

\[ h = -16t^2 + 18 \]

To find out when the egg hits the ground, we set \( h = 0 \) (the height when it hits the ground):

\[ 0 = -16t^2 + 18 \]

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

1. Rearrange the equation: \[ 16t^2 = 18 \]

2. Divide both sides by 16: \[ t^2 = \frac{18}{16} = \frac{9}{8} \]

3. Now take the square root of both sides: \[ t = \sqrt{\frac{9}{8}} = \frac{3}{\sqrt{8}} = \frac{3\sqrt{8}}{8} = \frac{3\sqrt{4 \cdot 2}}{8} = \frac{3 \cdot 2 \cdot \sqrt{2}}{8} = \frac{3\sqrt{2}}{4} \]

Using a calculator, \( \sqrt{2} \approx 1.414 \):

\[ t \approx \frac{3 \times 1.414}{4} \approx \frac{4.242}{4} \approx 1.0605 \]

Rounding to the nearest tenth:

\[ t \approx 1.1 \text{ seconds} \]

So, it took approximately 1.1 seconds for the egg to hit the ground.