A soccer player who is 27 feet from a goal attempted to kick the ball in into the goal. the flight of the ball is modeled by a parabola. the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. the goal has a height of 8 feet. will the soccer ball land in the goal?
Accepted Solution
A:
The parabola is facing downward that is why it is going to take the equation,
x² = -4ay If we take the point at which the maximum height is reached be the origin, the starting point of the parabola from the left is going to be (-15, -10). Substituting the values of x and y to the equation, (-15)² = -4(a)(-10) a = 5.625
The goal is at the point equal to (27 - 15, 8 - 10) or (12, -2). We are to substitute these values to the equation and see if the equation is satisfied. x² = -4(5.625)(y) 12² = -4(5.625)(-2) 144 ≠ 45