A soccer player kicks a ball from the ground to a maximum height of 12 m. The high point in the trajectory of the ball occurs at a distance of 18 m from the kicker. On the downward path, another player heads the ball at a height of 2.2 m from the ground.
a) What are the coordinates of the vertex for this situation?
b) How far from the kicker in the line of the trajectory must a player be to head the ball as described?
c)Describe at least one assumption you are making in using this model to determine the position of the player heading the ball.
a) y = max height = 12
x = point of max height = 18
b) vertex form of parabola
y =a (x-18)^2 + 12
0 = a ( 324) + 12 ( at x = 0 y = 0 so calculate 'a' values here)
-12/384 = a = - 1/32
y = - 1/32 (x-18)^2 + 12
2.2 = - 1/32 (x-18)^2 + 12 What value of x produces a y value of 2.2 m ?
x = 35.70 m from kickoff point this ignores air friction and assumes the ground is level playing field