Respuesta :
Answer:
a. The ball enters the green at Q (-13.46, -32.31)
b. 3.189s
c. 5.824s
d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey
Step-by-step explanation:
he rightmost edge is taken as the right end of the horizontal diameter
Coordinates of the hole at H:(0,0)
Coordinates of the ball B:(-40,-50)
Coordinates of the point the ball exits green P:(35,0)
So, the line joining B and P is given by
Looking for the gradient of the line B P we have
(x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50))
= 75/50=3/2
The line equation therefore = (y-(-50))/(x-(-50)) = 2/3
(y + 50)/(x+40) =2/3
y+50 = 2/3 (x+40)
The equation of a circle is given by
x^2+y^2 = 35^2
solving the two equations we have
x = ((3y+150)/2)-40 = 1.5y-35
Substituting the value of x into the above equations we have (1.5y-35)2 + y2 = 352
3.25×y2+105×y = 0
From where we have y×(3.25×y + 105) = 0
From where y = 0 or y = -105/3.25 = -32.31m
Also x = 35 or x = -13.46
The line intersects the circle at
Q:(-13.46,-32.31) and P:(35,0)
a. The ball enters the green at Q (-13.46, -32.31)
b. The ball enters the green after (length BQ)/Velocity
Where length BQ is given as
√((-13.46-(-40))2+(-32.31-(-50))2) = √(26.532+17.692) = 31.89ft
The ball enters after 31.89ft/10ft/s or 3.189s
c. To find out how long the ball spends inside the green we have
Q:(-13.46,-32.31) and P:(35,0)
Length QP2 = (-13.46-(35))2 + (-32.31- 0)2 = 3392.31 = 58.24m
Time spent in the green = 58.24/10 = 5.824s
d. The ball is closest to the cup at the point when the perpendicular from the cup intersects the line PQ
and this is at the center of the line PQ hence the locus of the point is
((-13.46 + (35-(-13.46))/2), (-32.31+(0-(-32.31))/2) = (10.77, -16.15)
This occurs at (√( (10.77-(-40))2 + (-16.15(-50))2))/10 = 61.02ft/10ft/s = 6.102s after the ball starts its journey
As the cup of the 9th hole in the golf course is located as the dead in the center of the milled green circular shape that is 70 feet. A ball follows the straight-line path and exists at the fright most edge.
- The rightmost edge is taken as per the right end of horizontal diameter. The coordinates of the hole at H: (0,0) B:(-40,-50) ball exits green P:(35,0)
- The line joining B and P is given by (x2-x1)/(y1-y2) =(35 –(-40))/(0-(-50)) = 75/50=3/2.
- Similarly, The ball enters the green at Q (-13.46, -32.31) , b. 3.189s , c. 5.824s, d. Closest point = (10.77, -16.15), it occurs 6.102s after the ball starts its journey.
Learn more about the hole of a golf course is located dead center in the middle.
brainly.com/question/2553954.
