Part a.
You need to solve the quadratic function h = -16t^2 + 60 t + 6 = 0
-16t^2 + 60 t + 6 = 0
Divide by 2, just to make the numbers easier
-8t^2 + 30t + 3 = 0
Use the quadratic formula to find the roots
t=[ -b ± √(b^2-4ac) ] /2a
t=[-30 ± √(30^2-4(-8)(3) ]/2(-8)
t=[-30 ± √(900 + 96) ]/(-16)
t=[-30 ± √(996) ]/(-16)
t=[-30 ± 31.56) ]/(-16)
t=[-61.56) ]/(-16) = 3.85 s
Part b)
h = -16t^2 + 60 t + 6
h (3) = -16(3)^2 + 60 (3) + 6 = -144 + 180 + 6 = 42 ft
