The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the
1 answer:
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Answer:
maximum height of 17.07 feet about 10.67 feet from the club
returns to the ground 21.33 feet away
Step-by-step explanation:
A graphing calculator can answer these questions easily.
The vertex of the quadratic ax²+bx+c is given by x=-b/(2a). For this quadratic function, the highest point is found at ...
x = -(3.2)/(2(-0.15)) = 32/3 = 10 2/3 . . . . feet horizontally from the club
The maximum height is the function value at that point.
h(10 2/3) = (-0.15(10 2/3) +3.2)(10 2/3) = 1.6(10 2/3) = 17 1/15
The ball reaches a maximum height of 17 1/15 feet at a horizontal distance of 10 2/3 feet from the club. The ball's flight is symmetrical about the peak, so it returns to the ground about 21 1/3 feet away.
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The answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
What is slope of a line segment ?
The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).
Let's solve the given parts based on the above data.
a.
The length of the line segment will be given by :
YZ =
YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}
YZ = √ (-8)² + 2²)
YZ = √68
YZ = 8.24 units
b.
The midpoint (say M) of the line segment will be given by :
M = ( )
M = [(2-6)/2 , (-3-1)/2]
M = ( -2 , -2 )
c.
And the equation of line passing through points Y and Z will be :
= m (
)
Let's calculate value of slope (m) firstly which will be :
m =() / (
)
m = ( -1 + 3 ) / (-6 - 2)
m = 2 / -8
m = -1 / 4
or
m = -0.25
Using the value of slope (m) : we get the equation of line as :
= - 0.25 (
)
or
(y + 3) = - 0.25 ( x - 2)
y + 3 = -0.25 x + 0.50
or
y + 0.25 x - 2.5 = 0
If we multiply by 4 throughout the equation ; then the equation of line can also be written as :
4y + x - 10 = 0
Therefore the answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
Learn more about line segment here ;
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