Mitch tossed an apple to kathy, who was on a balcony 40ft above him,
with an initial speed of 56ft/s. Kathy missed the apple on its way up,
but caught it on its way down. How long was the apple in the air? 
Formula: h = rt - 16t2

                                             h = rt - 16t2

r = initial speed = 56, so

                                             h = 56t - 16t2

We want to find the time when the apple was at a height of 40,
so we replace h by 40 and solve for t:

                                            40 = 56t - 16t2

Get 0 on the right

                               16t2 - 56t + 40 = 0

Factor 8 out of left side

                                8(2t2 -7t + 5) = 0

Factor the trinomial

                              8(t - 1)(2t - 5) = 0

Set each factor = 0 which contains a variable

Setting first factor = 0

                          t - 1 = 0 gives t = 1 second

Setting second factor = 0

                         2t - 5 = 0 gives t = 5/2 or 2.5 seconds.

The two answers are the times the apple was even with Kathy.
If Kathy had caught the apple on its way up, the answer would
have been 1 second.  But since she missed it then, but caught
it on its way back down, the answer is 2.5 seconds.

[The apple went 9 feet above her head before it started falling,
but you weren't asked for that information. But he threw it
rather hard, which is why she missed it on its way up. :-) ] 

Edwin
AnlytcPhil@aol.com