Editing Trajectory (section)

====Derivation of the equation of motion====
Assume the motion of the projectile is being measured from a [[free fall]] frame which happens to be at (''x'',''y'')&nbsp;=&nbsp;(0,0) at&nbsp;''t''&nbsp;=&nbsp;0. The equation of motion of the projectile in this frame (by the [[equivalence principle]]) would be <math>y = x \tan(\theta)</math>. The co-ordinates of this free-fall frame, with respect to our inertial frame would be <math>y = - gt^2/2</math>. That is, <math>y = - g(x/v_h)^2/2</math>.

Now translating back to the inertial frame the co-ordinates of the projectile becomes <math>y = x \tan(\theta)- g(x/v_h)^2/2</math> That is:

: <math>y=-{g\sec^2\theta\over 2v_0^2}x^2+x\tan\theta,</math>

(where ''v''<sub>0</sub> is the initial velocity, <math>\theta</math> is the angle of elevation, and ''g'' is the acceleration due to gravity).