The ball describes a parabola, as you can see in the attached picture. So, the point where the ball strike the ground is the point where the parabola meets the x axis. In fact, the x-axis is the set of points where y=0, which means that the ball has height 0 or -again- it hits the ground.
So, we have to set y=0 in our equation and look for the positive solution. We have
And the positive solution is
So that's the distance from the child where the ball strikes the ground.
Answer:
Given : The high school stadium contains a track that surrounds a soccer field. The soccer field is 100 yards long and 70 yards wide.
The school decided to cover the semicircles with grass to create a space for stretching and other activities.
To Find: area of one of the semicircles at either end of the track
How many square yards of grass will the school need to cover the entire circle?
Solution:
Diameter of semicircle = 70 yards
Radius of semicircle = 70/2 = 35 yards
Area of semicircle at one end = (1/2)πr²
= (1/2)(22/7)35²
= 1,925 sq yards
area of one of the semicircles at either end of the track = 1,925 sq yards
square yards of grass will the school need to cover the entire circle
= 2 x 1,925
= 3850 sq yards
distance around one of the semicircles at either end of the soccer field = πr = (22/7) 35 = 110 yards
distance around the inner lane of the track = 100 + 100 + 110 + 110
= 420 yards
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