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Suppose I have a projectile, fired at angle $\theta$, with velocity $v_0$, assuming it's only acted upon by gravity. How can I find an equation to enable me to plot the motion (vertical height against time) on a graph (I'll be doing this computationally)

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    $\begingroup$ It's a classical problem, you can find the solution in every Physics book. Are you interested to derive it by yourself? $\endgroup$ – user Nov 11 '18 at 21:24
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    $\begingroup$ Refer for example to Projectile motion. $\endgroup$ – user Nov 11 '18 at 21:25
  • $\begingroup$ The answer to this does not come from mathematics, but from physics ... $\endgroup$ – Bram28 Nov 11 '18 at 21:26
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You have to find the parametric equation of the trajectory.

With units in feet and seconds we get the following equations.

Note that your $$x(t)=(v_0 \cos \theta )t$$

and your $$y(t)= -16 t^2+(v_0 \sin \theta )t +x_0$$

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