So now we know how the position of an object in free fall depends on
time. But what if we want to know the shape of arc drawn out by the
object? We want to know how y depends on x.
Let's take the initial position of the object to be at the
origin 
. Then we just eliminate
time in eqs. 5.15 and 5.16. So first solve for
time in eq. 5.15, that gives 
. Substitute
this into 5.16 and we get:
This is the equation of a parabola. A stream of water, such as produced by a garden hose, or a fountain, gives us nice conformation of these parabolic shapes.
