Final answer:
The domain of the function h(t) = -16t² + 40t, representing the height of a ball over time, consists of all non-negative time values starting from when the ball is kicked. Therefore, the correct answer is (b) t > 0.
Step-by-step explanation:
The domain of a function is the set of all possible input values (usually time, in this case) for which the function is defined. In the context of real-world scenarios such as this one, where h(t) = -16t² + 40t represents the height of a ball over time, the domain would consist of all time values during which the ball is in the air. Since time cannot be negative in this context, the domain of the function will only include non-negative values of time that result in a non-negative height, meaning h(t) ≥ 0. Therefore, the correct domain is represented by option (b) t > 0, since time starts when the ball is kicked and continues until it lands on the ground, at which point the height would no longer be positive.