Answer:
The number is 623.
Step-by-step explanation:

The domain is the limits of the function. Since time doesnt go negative, start with 0. At time 0, the height is
-16(0)^2 + 144 = 144ft
Then, solve for t to find the upper limit for t, which is when the height is zero (since you're dropping the object).
-16t^2 + 144 = 0
-16t^2 = -144
t^2 = 9
t = sqrt(9)
t = 3
The domain is 0 to 3 seconds.
1/3 * 7/9 kg = (1 * 7)/(3 * 9) kg = 7/27 kg
He used 7/27 kg of sugar.