Question

Plz help! Actually Answer plz!

During halftime of a football ​game, a slingshot launches​ T-shirts at the crowd. A​ T-shirt is launched from a height of 4 feet with an initial upward velocity of 80 feet per second. The​ T-shirt is caught 41 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

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Answer:

time to max height: 2.5 seconds

max height: 104 ft

range of function: [4, 104]

Explanation:

The equation for ballistic motion is ...

h(t) = -16t^2 +v0·t +h0 . . . . where v0 is the initial upward speed and h0 is the initial height

For the given parameters, the height function is ...

h(t) = -16t^2 +80t +4

The time for maximum height is ...

-b/(2a) = -80/(2(-16)) = 2.5 . . . seconds

The maximum height is ...

h(2.5) = (-16·2.5 +80)(2.5) +4 = 104 . . . feet

The range of the function is from the minimum height (at launch) to the maximum height:

4 ft ≤ h(t) ≤ 104 ft.