MATH SOLVE

10 months ago

Q:
# 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

Thus, the ball will not land in the goal.

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

Thus, the ball will not land in the goal.