Students will explore quadratic functions in the form of a motorcycle jumping off of a ramp. Students will maximize the height of the jump and the airtime of the jump.
In Problem 1, students use a graphical model to explore the effect of setting the ramp at different angles to discover that the relationship between the angle of the ramp and the horizontal distance of the jump can also be described by a quadratic function. Students use this function to find the angle that maximizes the horizontal distance of the jump.
In Problem 2, students build their own model relating the angle of the ramp and the airtime of the jump, and then they use a similar process to discover that the airtime of the jump increases without bound as the angle of the ramp approaches 90°. Finally, they use their results to make recommendations for the rider.
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