example 5 model a dropped object with a quadratic function science competition for a science...
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EXAMPLE 5 Model a dropped object with a quadratic function
Science Competition
For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. How long does the container take to hit the ground ?
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EXAMPLE 5 Model a dropped object with a quadratic function
SOLUTION
h = – 16t 2 + h0 Write height function.
0 = – 16t 2 + 50 Substitute 0 for h and 50 for h0.
– 50 = – 16t 2 Subtract 50 from each side.
5016
= t2 Divide each side by –16.
5016+ = t Take square roots of each side.
+ 1.8 t Use a calculator.
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EXAMPLE 5 Model a dropped object with a quadratic function
ANSWER
Reject the negative solution, –1.8, because time must be positive. The container will fall for about 1.8 seconds before it hits the ground.
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GUIDED PRACTICE for Example 5GUIDED PRACTICE
What If? In Example 5, suppose the egg container is dropped from a height of 30 feet. How long does the container take to hit the ground?
20.
ANSWER about 1.4 sec