Answer:
0.447 sec
Explanation:
velocity = distance/ time
distance 'h' is a function of time 't' given by
[tex]h = 12t^{2} + 44t + 16[/tex]
⇒ differentiating equation
⇒ velocity = [tex]\frac{dh}{dt} = 24t + 44[/tex]
⇒ acceleration = [tex]\frac{d^{2}h }{dt^{2} }[/tex] = 24 [tex]\frac{ft}{sec^{2} }[/tex]
deceleration due to gravity = -9.8 m/[tex]sec^{2}[/tex] = Â - 9.8 x 3.281 = - 32.154 ft/ [tex]sec^{2}[/tex]
Net deceleration = 24 - 32.154 = - 8.15 ft/ [tex]sec^{2}[/tex]
at maximum height v = 0
[tex]v^{2}[/tex] = [tex]u^{2}[/tex] + 2ah
⇒  0 = [tex]44^{2}[/tex] + 2 (-8.15)h
⇒ h = 118.72 ft⇒
118.72 = 12[tex]t^{2}[/tex] + 44t + 16
⇒ [tex]12t^{2} +44t[/tex] - 102.72 = 0
⇒  t = -44 ± [tex]\sqrt{44^{2} - 4(12)(102.72) }[/tex]   / (2 x 12)
t = 0.447 sec
