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In this science competition challenge, students must create a container that protects an egg from breaking when dropped from a height of 50 feet. To determine how long it takes for the container to reach the ground, we can model the drop using a quadratic function. The height equation is derived from physics principles, allowing students to calculate the time of fall. This engaging project encourages creativity and application of mathematical concepts. Students must also consider variations, such as dropping from different heights, to explore design effectiveness.
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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 ?
50 = t2 5016 16 + = t + 1.8 t EXAMPLE 5 Model a dropped object with a quadratic function SOLUTION h = – 16t 2+ h0 Write height function. Substitute 0 for hand 50 for h0. 0 = – 16t 2 + 50 Subtract 50 from each side. – 50 = – 16t 2 Divide each side by –16. Take square roots of each side. Use a calculator.
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.
for Example 5 GUIDED PRACTICE GUIDED PRACTICE What If?In Example 5, suppose the egg container is dropped from a height of 30feet. How long does the container take to hit the ground? ANSWER about 1.4 sec
