The ball will hit the ground when h(t)=0 so
-1.85t^2+20t+1=0 using the quadratic formula for simplicity...
t=(-20±√407.4)/-3.7, since t>0
t=(-20-√407.4)/-3.7 seconds
t≈10.86 seconds (to nearest hundredth of a second)
....
How long will the ball be greater than 17m, h(t)>17
-1.85t^2+20t+1>17
-1.85t^2+20t-16>0
t>(-20+√281.6)/-3.7
t<(-20-√281.6)/-3.7 approximately...
t<9.94
t>0.87
0.87<t<9.94 to the nearest hundredth of a second
0.88≤t≤9.93
9.93-0.88=9.05
So the ball will be greater than 17m for about 9.05 seconds.
