I am building a game, where I have to plot a trajectory of a ball in 3D space, launched with an inital velocity **Sx, Sy, Sz**. [*I am using OpenGL and Android-NDK*]

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> Lets assume **Sz** is always **0**. And **Sx** and **Sy** values are known. 
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Now, I am able to plot a dotted trajectory properly along the path taken by the ball, under uniform gravity. But, the problem is that the distance between the points are NOT EQUIDISTANT, since I am plotting them at regular time intervals. 

So, the next step for me is to plot the trajectory at intervals (**tn**) such that my distance traveled (**d**) is always fixed. 

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> Now, assume I want to plot the **"nth"** trajectory point for every **"d"** units of distance. So, I need **'tn'** to plot it.
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I have tried solving this on white board, but the resulting equation for **'tn'** is too complex. And I could get this far :

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> **d^2 = dx^2 + dy^2;**
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> **dx = Sx \* t; | t = dx/Sx;**
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> **dy = Sy \* t + 1/2 (g) (t^2); | dy = Sy \* (dx/Sx) + 1/2 (g) ((dx/Sx)^2);**
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> So **t = 'gives me an equation that has a highest order of 4'**;
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I am hoping there must be a better way. Can anyone please help me derive a better equation for **'t'**.

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> Time **(tn)** = ?; 
>  Assume **tn = Tn - T(n-1)**; 
>  Where **'Tn'** is total time to cover **'n'** times **'d'** units of distance.
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> 
> In terms of :
>  **'d'** : is distance interval. (fixed);
>  **'sx'**: initial velocity along x axis (horizotal ground);
>  **'sy'**: initial velocity along y axis (against gravity **'g'**);
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Hope, I made thing clear enough. Please let me know if you need more information.

I tried this question in 'physics.stackexchange.com', but I was thinking this might be a more appropriate place to discuss, since I want a perspective of a game developers too.