Step-by-step explanation:
f(t) = -16t² + 126t
for what values of t did this function deliver 50 ft of height ?
50 = -16t² + 126t
-16t² + 126t - 50 = 0
the general solution to such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = t
a = -16
b = 126
c = -50
t = (-126 ± sqrt(126² - 4×-16×-50))/(2×-16) =
= (-126 ± sqrt(15876 - 3200))/-32 =
= (-126 ± sqrt(12676))/-32 =
= (-126 ± 112.5877436...)/-32
t1 = (-126 + 112.5877436...)/-32 = -13.41225644.../-32 =
= 0.419133014... ≈ 0.42 seconds
t2 = (-126 - 112.5877436...)/-32 = -238.5877436.../-32 =
= 7.455866986... ≈ 7.46 seconds
so, this means, right after launch the ticket reaches 50ft (from below) after 0.42 seconds, and then, when it falls back down, it will reach 50ft again (this time from above) after 7.46 seconds of flight time.
