A soccer player kicks a ball?
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. 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? Give the answer to two decimal places.
- davidLv 71 month ago
x = distance from kicker
y = height of ball
(0,0) <<< original place where ball is kicked
(18, 12) <<< hghest point
because of symmetry (36,0) should be another point .. except for the header
y = ax^2 + bx + c
0 = a(0) + b(0) + c .. c = 0
12 = a(18^2) + b(18)
0 = a(36^2) + b(36) ... b= -36a
12 = 324a + 18b
12 = 324a + 18(-36a) ... a = -12/324 = -1/27
b = +4/3
. . . y = -(1/27)x^2 + (4/3)x <<< quadratic
y = 2.2 .. x = ? . .
2.2 = -(1/27)x^2 + (4/3)x <<< solve for x
x = 34.2665 m
y = -(1/27)x^2 + (4/3)x for 0 < x < 34.2665
the quadratic must have a limited domain because of the header