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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?

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Answer:

The ball will land inside the goal.

Explanation:

Given : The flight of the ball is modeled by a parabola.

To find : Will the soccer ball land in the goal?

Solution :

Let the equation of the parabola be,


y=a(x-h)^2+k

Where, (h,k) are the vertex of the parabola,

According to question,

A soccer player who is 27 feet from a goal.

Let A be the point where player stand i.e, (27,0)

The height of the goal is 8 feet.

Let B be the point of height of goal i.e, (0,8)

The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.

The distance from goal to the distance 15 feet away from the player is

27-15=12 feet

Let C be the point with maximum height i.e, (12,10)

C is the vertex of the parabola and A is the point on the parabola.

Then, The equation of parabola is


y=a(x-12)^2+10

Point A satisfy the equation,


0=a(27-12)^2+10


0=a(15)^2+10


a=-(10)/(225)

Substitute back in equation,


y=-(10)/(225)(x-12)^2+10

Now, we find the y-intercept of the equation i.e, x=0,


y=-(10)/(225)(0-12)^2+10


y=-(10)/(225)(144)+10


y=3.6

If the y-intercept is greater than 8 then the ball will land outside the goal.

If the y-intercept is less than 8 then the ball will land inside the goal.

As 3.6<8

Therefore, The ball will land inside the goal.

Refer the attached figure below.

A soccer player who is 27 feet from a goal attempted to kick the ball in into the-example-1
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