Question

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A football is kicked straight up into the air from 3 feet above the ground with an initial velocity of 208 ft/s. The function that models the ball's height is: h(t) = -16t^2 + 208t + 3.
a) Find how long it takes for the football to reach its maximum height.

b) Determine how long the football was in the air (approximately). Why might this not quite be accurate?

c) Determine the maximum height of the football.

Answer 1

• a) 6.5 seconds
• b) 13 seconds
• c) 679 ft

Explanation:

Given function:

• h(t) = -16t^2 + 208t + 3

a) Maximum height is the vertex. The ball reaches the maximum after:

• h = -208/2(-16) = 6.5 seconds

b) Time the ball was in the air:

• -16t^2 + 208t + 3 = 0

Solving we get approximately t = 13 seconds

c) Maximum height is at vertex, we found t above:

• h(6.5) = -16(6.5)^2 + 208*6.5 + 3 = 679 ft