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In this science competition, students are tasked with creating a container to protect an egg during a drop from a height of 50 feet. Participants will model the drop using quadratic functions to predict the fall time. Using the equation ( h = -16t^2 + h_0 ), they will calculate how long it takes for the container to hit the ground. For instance, by substituting 50 for initial height ( h_0 ), they discover that the drop will take approximately 1.8 seconds. This hands-on project encourages innovation and understanding of physics principles in a fun and engaging way.
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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 ? EXAMPLE 5 Model a dropped object with a quadratic function Science Competition
50 = t2 5016 16 + = t2 + 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.
30 3016 16 + = t2 + 1.4 t = t2 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? SOLUTION h = – 16t 2+ h0 Write height function. Substitute 0 for hand 30 for h0. 0 = – 16t 2 + 30 Subtract 30 from each side. – 30 = – 16t 2 Divide each side by – 16. Take square roots of each side. Use a calculator.
for Example 5 GUIDED PRACTICE GUIDED PRACTICE ANSWER Reject the negative solution, – 1.4, because time must be positive. The container will fall for about 1.4 seconds before it hits the ground.
