Question

During halftime of a soccer game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with an initial upward velocity of 72 ft. Per second. The T-shirt is caught 34 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time.

Answer 1

Hi,

During halftime of a soccer game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with an initial upward velocity of 72 ft. Per second. The T-shirt is caught 34 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range of the function that models the height of the T-shirt over time.

Write the general equation that represents height of the t-shirt as a function of time.

f(t) = -16$t^{2}$ + 72t + 5

2. What is the maximum height of the t-shirt?

$t = \frac{-72}{2(-16)} = 2,25$                         $f(2,25) = -16(2,25)^{2} + 72(2,25) + 5$

                                                                $= 86 feet$

1. How long will it take the t-shirt to reach its maximum height?

2,25 secondes

3. The range describes which values of the graph? What would the range of this graph be? (Write in inequality and interval notation).

height (y)

5 ≤ y ≤ 86        [ 5,86 ]