The punter on a special team unit kicks a football upward from the ground with an initial velocity of 63 feet per second. The height of the football stadium is 70 feet. The height of an object with respect to time is modeled by the equation:

where g is -32 ft/second squared, v is the initial velocity, and s is the initial height.

1. Write a function that models this situation.

2. Sketch and describe the graph of this function.

3. At what times will the football be the same height as the top of the stadium? Explain.

4. Suppose the punter's initial velocity is 68 feet per second. At what times will the football be the same height as the top of the stadium? Justify.

Guest Jun 7, 2022

#1**+1 **

1) The function is

h(t) = -16t^2 + vt + s =

h(t) = -16t^2 + 63t

2) Here's the graph (in x instead of t) : https://www.desmos.com/calculator/96nhz6lqgq

3) Note that with the given function, the ball never rises above ≈ 62 ft

4) If the punter's initial velocity is 68 ft/s we have the graph of -16t^2 + 68t : https://www.desmos.com/calculator/2bn74gqnob

The ball will be > than the stadium height between 1.75 and 2.125 sec

CPhill Jun 7, 2022