Question 1181908
f(t)=-5t^2+80
maximum height is at t=-b/2a or -80/-10 or 8 seconds. 
f(8)=-320+640=320 feet.
since the graph is symmetrical around t=8 seconds,, it hits the ground in 16 seconds.
-5t^2+80t=275
-5t^2+80t-275=0
-5(t^2-16t+55)=0
(t-11)(t-5)=0
at 5 seconds.  That is for the first time, which is how I interpret the question, but it also will occur at 11 seconds on the way down.

{{{graph(300,300,-10,20,-50,350,275,320,-5x^2+80x)}}}