Answer:
The required domain is 0.5 < t < 2.
Step-by-step explanation:
Find the time of maximum height by converting to vertex form:
f(t) = −16t^2 + 16t + 32
f(t) = -16(t^2 - t) + 32
= -16 [(t - 0.5)^2 - 0.25)]+ 32
So the time at maximum height = 0.5 seconds.
To find the time t when it falls to the ground:
-16t^2 + 16t + 32 = 0
-16(t^2 - t - 2) = 0
-16(t - 2)(t + 1) = 0 giving t = 2, -1 ( we ignore the -1).
t = 2 seconds.
Therefore the answer is 0.5 < t < 2.
