Question

A player kicks a soccer ball from a height of 2 feet. The ball reaches A maximum height of 20 feet after traveling 40 feet horizontally. And is caught by the goalkeeper 70 feet from where it was kicked. The path of the ball can be modeled by a parabola where why is the height in feet an exit the horizontal distance traveled in feet. At what height is the goalkeeper catch the ball?

Answer 1

The height is 9.875 feet from which the goalkeeper catches the ball.

The player kicks soccer from a height of 2 feet

x = 0 and y = 2

Maximum height of 20 feet after traveling 40 feet

x = 40, y = 20

So let y = a(x - 40)² + 20  ( the path of parabola)

Since x = 0 , y = 2

So, 2 = a(0 - 40)² + 20

2 = 1600a + 20

-18 = 1600a

a = - 9/800

Thus, y = -9/800(x - 40)² + 20

Since the soccer is caught by the goalkeeper 70 feet from where it was kicked

x = 70

So at this time,

y = -9/800 ( 70 - 40)² + 20

  = -9/800 × 900 + 20

  = - 81/8 + 20

  = 79/ 8

  = 9.875 feet

Therefore the height at which the goalkeeper catches the ball is 9.875 feet.

To know more about the height refer to the link given below:

brainly.com/question/27030273

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