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16 Nov 2019

A quarterback throws a football from a heigh of 6 feet with an initial velocity of 20 feet per second. The height, h, of the ball at time t seconds can be represented by the equation h(t) = -16t2 + 20t + 6. If the ball is caught at 2 feet, find the range of the function.

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Bunny Greenfelder
Bunny GreenfelderLv2
21 May 2019

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Matt and his friends are enjoying an afternoon at a baseball game. A batter hits a towering homerun, and
Matt shouts, “Wow, that must have been 110 feet high!” The ball was 4 feet off the ground when the batter
hit it, and the ball came off the bat traveling vertically at 80 feet per second.


a. Model the ball’s height h (in feet) at time t (in seconds) using the projectile motion model h(t) = 16t2 + v0t + h0 where v0 is the projectile’s initial vertical velocity (in feet per second) and h0 is the projectile’s initial height (in feet). Use the model to write an equation based on Matt’s claim, and then determine whether Matt’s claim is correct.


b. Did the ball reach a height of 100 feet? Explain.


c. Let hmax be the ball’s maximum height. By setting the projectile motion model equal to hmax, show
how you can find hmax using the discriminant of the quadratic formula.


d. Find the time at which the ball reached its maximum height.


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