Question

During halftime of a football game a slingshot launches T-shirts at the crowd a T-shirt is launched from a height of 6 feet with an initial upward velocity of 72 ft./s the T-shirt is cot 45 feet above the field how long will it take the T-shirt to reach the maximum height what is the maximum height what is the range of the function that models the height of the T-shirt overtime

Answer 1

2.25 seconds

87 feet

[6, 87]

Explanation:

The height of a projectile is:

h(t) = -16t² + vt + s

where v is the initial vertical velocity and s is the initial height.

Here, v = 72 and s = 6.

h(t) = -16t² + 72t + 6

This is a downwards parabola. The maximum is at the vertex.

t = -b / (2a)

t = -72 / (2×-16)

t = 2.25

h(2.25) = 87

It takes 2.25 seconds to reach the maximum height of 87 feet.

The range is from the lowest height (6 feet) to the maximum height (87 feet). In interval notation:

[6, 87]