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.
+36916 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
