Baby asked in Science & MathematicsMathematics · 1 month ago

# The distance from the edge of the centre circle toward the goal and y is the height of the ball.?

A soccer player kicks the ball from a position 17.5 m in front of the goal line. The quadratic function y=-0.05(x-20)(x-40)   describes the path of the ball, where x is the distance from the edge of the centre circle toward the goal and y is the height of the ball.

a. What are the coordinates of the points where the ball theoretically touches the ground?

Update:

b. What is the maximum height of the ball during its flight

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• Ash
Lv 7
1 month ago

y=-0.05(x-20)(x-40) .....(1)

When the ball touches the ground, y = 0

So we need to find x, when y = 0

Now plug in (1)

0=-0.05(x-20)(x-40)

0 = (x-20)(x-40)

x = 20 and x = 40

The ball touches the ball at 40 m from the edge of the centre circle

b. At max height vertical velocity = 0

vertical velocity = y'

y' = -0.05[(x-40) + (x-20)]

0 =  -0.05(2x-60)

2x-60 = 0

2x = 60

x = 30

At x=15, find y

y = -0.05(30-20)(30-40) = 5 m

Max height of the ball = 5 m