Question 1157115
The function is f(t)= -16t^2+167t+114, the first for acceleration due to gravity, the second for initial speed, the third for initial height.
maximum height t is -b/2a or -167/-32-5.22 sec
height is 549.76 feet using 5.22.
set the equation = to 122
then it becomes -16t^2+167t-8=0
t=(-167+/- sqrt (167^2-512)/-32; sqrt term is 27377 and that equals+/- 165.46
t=-1.54/-32 or 0.048 sec
t=-332.46/-32 or 10.39 sec
That interval is 10.34 sec (rounded)

hits the ground when original equation equals 0.
t=(-167+/- sqrt (35185))/-32; -167+/-187.58=-354.58
divide by -32 and 
t=11.08 sec



{{{graph(300,300,-10,15,-50,600,-16x^2+167x+114,122)}}}