Need Help Solving TWO Word Questions

Question

I need help solving these TWO questions please. I'm stuck.

1. An object is launched directly overhead at 36 meters per second. The height (in meters) of the object is given by h(t) = -16t^2 + 36t + 5, where t is the time (in seconds) since the object was launched. For how many seconds is the object at or above a height of 25 meters?
2. A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h(t) = -6t^2 +24t +14, where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height?

Answer 1

h(t)-16t^2 +36t + 5 = 25

16t^2 -36t -5 = -25

16t^2 -36t +20 = 0

4t^2 -9t + 5 =0

(t-1)(4t-5) = 0

t= 1, 5/4

for a quarter second, from 1 second to 1 1/4 second, the height is > 25 feet

h(t) =-6t^2 +24t + 14

max height is when the derivative = 0

h'(t) = -12t +24 = 0

t = 24/12 = 2 seconds

max h = h(2) = -6(2^2) +24(2) +14

= -24 +48 +14 = 38 feet