Question

The height

Answer 1

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

$-\dfrac{1}{14}x^2+6x+3=0 \iff x=42\pm\sqrt{1806}$

And the positive solution is

$42+\sqrt{1806}$

So that's the distance from the child where the ball strikes the ground.