SOLUTION: A football initially on the ground is kicked in the air and follows a parabolic path after 2 seconds the football is 6 meters off the ground it reaches a maximum height of 8 meters
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Question 675395: A football initially on the ground is kicked in the air and follows a parabolic path after 2 seconds the football is 6 meters off the ground it reaches a maximum height of 8 meters after 4 seconds . Find the height of the football 7 seconds after the ball is kicked? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A football initially on the ground is kicked in the air and follows a parabolic
path after 2 seconds the football is 6 meters off the ground it reaches a
maximum height of 8 meters after 4 seconds.
Find the height of the football 7 seconds after the ball is kicked?
:
Using the form y = ax^2 + bx + c, where, y is the height in meters,
x = time in seconds, the ball starts at ground level therefore c = 0
:
Two ordered pairs to find a, and b
x=2; y=6
4a + 2b = 6
and
x=4, y=8
16a + 4b = 8
:
Use elimination, multiply the 1st equation by 2, subtract from the 2nd equation
16a + 4b = 8
8a + 4b = 12
----------------subtraction eliminates b, find a
8a = -4
a = -4/8
a = -.5
:
Find b using the 1st original equation
4(-.5) + 2b = 6
-2 + 2b = 6
2b = 6 + 2
b = 8/2
b = 4
:
The equation: y = -.5x^2 + 4x
Find the height when x = 7
y = -.5(7^2) + 4(7)
y = -24.5 + 28
y = 3.5 meters after 7 seconds
:
Graphically
