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Gheaton1889
08.10.2019 •
Physics
Afootball player kicks a football downfield. the height of the football increases until it reaches a maximum height of 15 yards, 30 yards away from the player. a second kick is modeled by f(x)=−0.032x(x−50), where f is the height (in yards) and x is the horizontal distance (in yards). compare the distances that the footballs travel before hitting the ground.
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Ответ:
Explanation:
The given function is
To find the distances that the second football travels, we need to find the vertex of its movement, because it's movement has a parabola form. The quadratic expression is
Where
and ![b=1.6](/tpl/images/0299/0594/7ec6d.png)
The vertex has coordinates of
, where
Replacing values, we have
Then,![k=f(h)](/tpl/images/0299/0594/f8ec9.png)
Which means the maximum height of the second football is 20 yards. That means it travels 40 yards vertically.
Now, its horizontal distance can be found when![f(x)=0](/tpl/images/0299/0594/ce73d.png)
So, its horizontal distance is 500 yards.
Comparing the distances between the footballs.
Ball 1Horizontal distance of 30 yards.
Vertical distance of 30 yards.
Ball 2Horizontal distance of 500 yards.
Vertical distance of 40 yards.
If we find their difference, it would be
Horizontal: 500 - 30 = 470 yards.
Vertical: 40 - 30 = 10 yards.
Therefore, the second ball traveled more distance, horizontally and vertically.
Ответ: