(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle is subject to a constant force F on +x direction. At t = 0, it is located at origin with velocity v_{o}in +y direction.

2. Relevant equations

Determine the trajectory of the particle. x(t),y(t),z(t)

3. The attempt at a solution

[tex]\vec{p}= \int \vec{F} dt[/tex]

[tex]\vec{p} = \vec{F}t + constant[/tex]

At t=0

[tex]\vec{p} = \gamma mv_{o}[/tex]

[tex]\vec{p} = Ft\hat{x} + \gamma mv_{o}\hat{y}[/tex]

what should I do next? should I integral over [tex]p_{x}[/tex] and [tex]p_{y}[/tex] separately? Is that so, what are the exact steps?

I tried using

[tex] p_{x} = \frac{mu_{x}}{\sqrt{1-\frac{u^{2}_{x}}{c^{2}}}} = Ft[/tex]

[tex]x(t) = \frac{mc^{2}}{F} (\sqrt{1+\frac{Ft}{mc}^{2}} -1) [/tex]

what about y(t)? it seems it is a linear with t. I don't know where I get wrong.

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# (special relativity)Trajectory under constant ordinary force

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