Question 907280
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Your initial velocity is given as 32 ft/sec and your initial position (the rooftop) is given as 195 feet.  Hence, the position function that describes your situation is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ s(t)\ =\ -16t^2\ +\ 32t\ +\ 195]


Your problem is to determine for what range of values of *[tex \Large t] is *[tex \Large s(t)] more than the height of the roof.  In other words *[tex \Large s(t)\ >\ 195], hence you need to solve the quadratic inequality:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -16t^2\ +\ 32t\ +\ 195\ >\ 195]


Of course, this all assumes that your hand, at the time you released the ball, was exactly at the level of the rooftop.  If you are actually more than zero feet tall such that your hand was *[tex \Large h] feet above the rooftop when you released the ball, then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -16t^2\ +\ 32t\ +\ 195\ +\ h\ >\ 195] 


is the inequality that you need to solve.  In that case, ignore any negative values of *[tex \Large t] because you don't really care what was going on <i>before</i> you threw the ball, do you?


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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