Question 211526: from the center of the 20yd (60ft) line, a football player attempts to make a field goal by kicking the ball directly toward the goal posts, which are 90ft away. The goal-post crossbar is 10 ft above the ground. The ball reaches its highest altitude of 32 ft at a point 48 ft from where it was kicked.
a. make a sketch showing the path of the football. if the point from which the ball is kicked is the origin of a coordinate plane, find the equation of the parabolic path of the football.
b. will the kicker make the field goal?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! An interesting problem for the football season
:
from the center of the 20yd (60ft) line, a football player attempts to make a
field goal by kicking the ball directly toward the goal posts, which are 90ft
away.
The goal-post crossbar is 10 ft above the ground.
The ball reaches its highest altitude of 32 ft at a point 48 ft from where it was kicked.
:
a. make a sketch showing the path of the football.
if the point from which the ball is kicked is the origin of a coordinate plane,
find the equation of the parabolic path of the football.
:
We have two sets of coordinates, we can make an equation from that
x=48, y=32 (vertex, highest point is half way to the x intercept (0)
and
x=96, y=0 where the ball hits the ground
:
using: ax^2 + bx = y
x=48, y=32
2304a + 48b = 32
and
x=96, y=0
9216a + 96b = 0
:
Find a & b, multiply the 1st equation by 2, subtract the 2nd equation
4608a + 96b = 64
9216a + 96b = 0
------------------Eliminates b
-4608a = 64
a = 
a = -.01389
:
find b using the 1st equation:
2304(-.01389) + 48b = 32
-32 + 48b = 32
48b = 32 + 32
b = 
b = 1.333
:
The equation: y = -.01389x^2 + 1.333x
looks like this:
Note the highest point: 48, 32
:
b. will the kicker make the field goal?
Find the value of y when x=90
y = -.01389(90^2) + 1.333(90)
y = -112.5 + 120
y = 7.5 ft, No, it will go under the cross bar which is 10 ft
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