Question

A model rocket is launched with an initial upward velocity of 126 ft/s. The rocket's height h (in feet) after 1 seconds is given by the following
=126t-16t^2
Find all values of t for which the rocket's height is 50 feet.
Round your answers) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

Answer 1

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.