Question

a person shoots an arrow vertically into the air from a height of 6 feet with an initial velocity of 96 feet per second. the height, h, in feet above the ground, at any time, t (in seconds), is modeled by h(t) = 6 + 96t - 16t². a. it indicates the distance covered by the arrow before hitting the ground. b. it indicates the height of the arrow when it hits the ground. c. it indicates the height of the arrow when it is shot. d. it indicates the maximum height of the arrow. d) what are the practical domain and practical range in this situation? choose the correct answer below. a. the practical domain is the time the arrow starts (0 seconds) to the maximum height of the arrow. the practical range is the distance that the arrow starts from the ground (0 feet) to the time it takes to reach the ground. b. the practical domain is the time the arrow starts (0 seconds) to the time it takes to reach the ground. the practical range is the distance that the arrow starts from the ground (0 feet) to the minimum height of the arrow. c. the practical domain is the time the arrow starts (0 seconds) to the minimum height of the arrow. the practical range is the distance that the arrow starts from the ground (0 feet) to the time it takes to reach the ground. d. the practical domain is the time the arrow starts (0 seconds) to the time it takes to reach the ground. the practical range is the distance that the arrow starts from the ground (0 feet) to the maximum height of the arrow.

Explanation:

1. Practical Domain: The domain of a function in a real - world context (practical domain) for the height of the arrow as a function of time \(h(t)=6 + 96t-16t^{2}\) is the set of all valid input values (time \(t\)). The arrow is shot at \(t = 0\) and stops being in the air when it hits the ground (when \(h(t)=0\)). So the practical domain is from \(t = 0\) (start time) to the time \(t\) when \(h(t)=0\) (time when it hits the ground).
2. Practical Range: The range of a function in a real - world context (practical range) for the height function \(h(t)\) is the set of all valid output values (height \(h\)). The arrow starts at a height of 6 feet (when \(t = 0\), \(h(0)=6\)) and rises to a maximum height and then falls back to the ground (\(h = 0\)). But the minimum height in the practical sense (while the arrow is in the air) is 0 (when it hits the ground) and the maximum height is the peak height of the parabola \(h(t)=- 16t^{2}+96t + 6\) (since the coefficient of \(t^{2}\) is negative, the parabola opens downwards, and there is a maximum point). So the practical range is from the initial height (or 0, since it hits the ground) up to the maximum height of the arrow. Option D correctly describes the practical domain (time from start to when it hits the ground) and practical range (height from ground level (0) to maximum height).

Answer:

D. The practical domain is the time the arrow starts (0 seconds) to the time it takes to reach the ground. The practical range is the distance that the arrow starts from the ground (0 feet) to the maximum height of the arrow.