Using a Falling Object Model
An engineering student is in an "egg dropping contest." The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg's container to hit the ground? Assume there is no air resistance.
Solution
Write an equation to model the egg container's height h as function of time t, where the initial height .
s Write falling object model.
32 Substitute 32 for s.
The falling object model for the egg container is
Method 1
MAKE A TABLE One way to solve the problem is to find the height h for different values of time t in the function . Organize the data in a table. The egg container will hit the ground when .
From the table, you can see that between 1.4 and 1.5 seconds. The egg container will take between 1.4 and 1.5 seconds to hit the ground.
Method 2
USE AN EQUATION. Another way to approach the problem is to solve the quadratic equation for the time t that gives a height of feet.
h = Write falling egg model.
0 = Substitute 0 for h.
Subtract 32 from each side.
Divide each side by -16.
Find positive square root.
Use a calculator.
The egg container will hit the ground in about 1.4 seconds. You can ignore the negative square root, because -1.4 seconds is not a reasonable solution.