# Projectiles / Parabola calculations

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Hi This is my first post to gamedev.net so if I'm breaking any rules let me know and I'll straighten up my act I have a problem where I am firing a projectile from a point (sx,sy) and the target point is fixed (tx,ty). vix is known and fixed aswell. Now I want to work out the initial Y velocity (viy). I'm aware of the simple equation for getting y over time (t) y = viy * t + 0.5 * g * t^2; but I was hoping for an almost as easy solution to getting viy with the variables known that I have said above. Thanks very much

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I'm not sure of any other way other than this one, however...

$V_{i,y} = \frac{-g(X_{2}-X_{1})}{2V_{i,x}}$

If you know vix, sx, and tx, then you know that the time it takes for the projectile to make its course is t = (tx - sx) / vix. Then plug it into the previous equation and solve for viy (resulting in viy = -g*t/2).

• I'm not sure I understand what it is you are trying to find.

If you are trying to calculate the initial y-velocity:
You shouldn't have to right? If you fire the projectile, you should know at which velocity it was shot.

If you are trying to find the final y-velocity:
Use Vf = V0 - g*t and plug in the final time for t.

If you are trying to calculate the velocity as a function of time:
You can do this using the same equation as before or you can try a different approach. Rather than simply plotting a parabola using your equation
y = viy * t + 0.5 * g * t^2
you could choose a time step dt and do the following:

float x, y, vx, vy, ax, ay, dt, v0x, v0y;dt = 0.01f;v0x = 10.0f;v0y = 10.0f;ay = -9.8f;// take a time stepvx += ax * dt;vy += ay * dt;x += vx * dt;y += vy * dt;

This method is a simplified version of Euler integration and will yield a similar result. Using this method, you could always know the velocity in the x and y direction through vx and vy.

If none of these are what you were looking for, then please clarify. :)

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Thankyou for the responses guys fastcall your solution worked perfectly thankyou :)
now I just need to work out how to do this when the start and end points are not have the same y value
If you have any more nibbles of genius I'd love for you to share them!

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