A soccer player kicks a ball from the ground to a maximum height of 11 m. the high point in the trajectory of the ball occurs at a distance of 16 m from the kicker. on the downward path, another player heads the ball at a height of 1.9 m from the ground.

Question

a. write a quadratic function that models the 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 any assumptions you are making in using this model to determine the position of the player heading the ball.

Answer 1

a) since the vertex is at (16,11), the x-intercepts are at x=0 and x=32:
y = ax(x-32) where a<0

11 = a*16^2
a = 11/256

y = 11/256 (32-x^2)

b) now just solve for x when y=1.9

c) the ball can be going up or down when the player heads it.

Answer 2

Thank you so much :)