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!

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=

16t2+s.
To the nearest tenth of a second, how long did it take for the egg to hit the ground?
seconds

1 answer

To solve the problem, we start by using the given formula for the height of an object dropped from a height \( s \):

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

In this scenario, \( s = 18 \) feet (the height from which the egg is dropped) and we are looking for the time \( t \) when the egg hits the ground. At that point, the height \( h \) will be \( 0 \) feet.

We set the formula equal to zero to find \( t \):

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

Next, we rearrange the equation to solve for \( t \):

\[ 16t^2 = 18 \]

\[ t^2 = \frac{18}{16} \]

\[ t^2 = \frac{9}{8} \]

Now, we take the square root of both sides to solve for \( t \):

\[ t = \sqrt{\frac{9}{8}} = \frac{3}{\sqrt{8}} = \frac{3}{2\sqrt{2}} = \frac{3\sqrt{2}}{4} \]

To find a numerical value for \( t \), we can calculate it approximately:

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

Rounding that to the nearest tenth of a second, we find:

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

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