I've been studying this rather interesting article about projectile motion in special relativity. The thing is, I can't understand how the author found the trajectory function. He says that he did it by solving the following parametric equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x(t)=\frac{cp_0cos\theta}{F}ln\left \{ \frac{\sqrt{E_0^2+c^2P^2(t)-c^2p_0^2sen^2\theta}+cP(t)}{E_0-cp_0sen\theta} \right \}\\\\

y(t)=\frac{1}{F}\left \{ E_0-\sqrt{E_0^2+c^2P^2(t)-c^2p_0^2sen^2\theta} \right \}[/tex]

For which he found the following function:

[tex]y(x)=\frac{E_0}{F}-\frac{E_0}{F}cosh\left [ \frac{Fx}{p_occos\theta} \right ]+\frac{p_0csen\theta}{F}senh\left [ \frac{Fx}{p_0ccos\theta} \right ][/tex]

I'm having some trouble with this calculation because of that [itex]cP(t)[/itex] term. I've tried backtracking as well, but it didn't work. I'm feeling stupid. :(

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# Trajectory function of projectile motion

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