Finding the Equation of a Trajectory for Projectile Motion
This comes up every so often. I get a situation (usually, it’s a video analysis problem) in which I can’t rely on the time data. This usually happens when you can see the motion of a projectile, but the middle part (or all of it) is in “slow motion”.
Before looking at the trajectory equation, let’s review what I would normally do for a video analysis. After collection (x,y,t) data in each frame, I could make two plots. I could plot the horizontal position vs. time. This should be a straight line (because there would be zero acceleration) and the slope of this line would be the horizontal velocity.
It would look like this plot of the horizontal position of Red from Angry Birds (from the game). Full analysis here.
The second thing I could do is to plot the vertical position vs. time. This should be a parabola. From the quadratic equation fit of this data, I can find the vertical acceleration. Again, here is an example from Angry Birds.
