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) determine the maximum height the arrow will attain.
150 feet
b) approximately when will the arrow reach the ground?
after approximately 6.06 seconds the arrow will reach the ground.
(type an integer or decimal rounded to the nearest hundredth as needed.)
c) what is the significance of the vertical intercept? choose the correct answer below.
○ 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.

Explanation:

The vertical intercept of a function \( h(t) \) occurs when \( t = 0 \). For the height function \( h(t)=6 + 96t-16t^{2} \), when \( t = 0 \) (the time when the arrow is shot), \( h(0)=6 \), which is the initial height of the arrow. Option A is incorrect as the vertical intercept is not about distance covered before hitting the ground. Option B is incorrect because when the arrow hits the ground, \( h(t) = 0 \), not the vertical intercept. Option D is incorrect as the maximum height is found by vertex formula or calculus, not the vertical intercept. So the correct answer is C.

Answer:

c) C. It indicates the height of the arrow when it is shot.