A football kicker boots the ball from the 15 yard line to the 35 yard line. The equation can be modeled by the the following: y = - .054(x - h)(x - k).....where h and k are where the football lands (x-intercepts). What was the maximum height that the football reached?

Answers

Answer 1

Answer:

The maximum height that the football reached = 5.4 yards (16.2 feet)

Step-by-step explanation:

The initial location of the ball = 15 yard line

The final location of the ball = 35 yard line

The equation of the ball's motion can be modeled as follows;

y = -0.054·(x - h)·(x - k)

Where;

h and k are the x-intercepts which are the points where the ball lands or where the ball is in contact with the ground

Given that the kicker kicks the ball from the ground on the 15 yard line and the ball lands on the ground at the 35 yard line, we can write

h = 15 yard line

k = 35 yard line

Therefore;

y = -0.054·(x - 15)·(x - 35) = -0.054·x² + 2.7·x-28.35

The maximum height is found by differentiating the function with respect to x and equating the result to 0 as follows;

d(-0.054·x² + 2.7·x-28.35)/dx = 2.7 - 0.108·x = 0

x = 2.7/0.108 = 25

Therefor, at the maximum point, we have;

x = 25

∴ y = -0.054·(25 - 15)·(25 - 35) = -0.054×10×(-10) = 5.4

The maximum height that the football reached = 5.4 yards = 16.2 feet.


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Answers

Answer:

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Answer:

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Answer:

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Answer:

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Answer:

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Step-by-step explanation:

Answer:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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