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maxonik [38]
2 years ago
10

A football is kicked toward an end zone with an initial vertical velocity of 30 ft/s. The function h(t) = -16+ 30t models the he

ight h (in feet) of the football at time t (in seconds). Which statement about the height of the football is true? A.The football does not reach a height of 15ft B. The football reaches a height of exactly 15ft C.The football reaches a height that is greater than 15ft
Mathematics
1 answer:
Ulleksa [173]2 years ago
8 0

Answer:

A. The football does not reach a height of 15ft

Step-by-step explanation:

Given

h(t) = -16t^2 + 30t

Required

Determine which of the options is true

The option illustrates the height reached by the ball.

To solve this, we make use of maximum of a function

For a function f(x)

Such that:

f(x) = ax^2 + bx + c:

f(\frac{-b}{2a}) = maximum/minimum

i.e we first solve for \frac{-b}{2a}

Then substitute \frac{-b}{2a} for x in f(x) = ax^2 + bx + c

In our case:

First we need to solve \frac{-b}{2a}

Then substitute \frac{-b}{2a} for t in h(t) = -16t^2 + 30t

By comparison:

b = 30

c = -16

\frac{-b}{2a} = \frac{-30}{2 * -16}

\frac{-b}{2a} = \frac{-30}{-32}

\frac{-b}{2a} = \frac{30}{32}

\frac{-b}{2a} = \frac{15}{16}

Substitute \frac{15}{16} for t in h(t) = -16t^2 + 30t

h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})

h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}

h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}

h(\frac{15}{16}) = \frac{-225 + 450}{16}

h(\frac{15}{16}) = \frac{225}{16}

h(\frac{15}{16}) = 14.0625

This implies that the maximum height reached is 14.0625ft.

So, the option that answers the question is A because 14.0625 < 15

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