I am working on a series of equations to calculate the trajectory of a projectile in reverse. For example, given the ground impact angle and velocity, calculate the flight of the projectile. Here is the equation to calculate the drag on a projectile in normal flight (not reversed yet):
$$ x_2=x(1-k\sqrt{x^2+y^2}) $$ $$ y_2=y(1-k\sqrt{x^2+y^2}) $$
$x$ and $y$ are the before-drag velocities, and $k$ is a constant that includes the fluid density, reference area, drag coefficient, and timestep. The result, $x_2$ and $y_2$, are the after-drag velocities. On my graphing calculator, including these functions in a program creates a nice-looking trajectory. However, to reverse the formula, I need to solve the above equations for $x$ and $y$. Given the resulting velocity, find the velocity at the previous timestep. I am at a loss on how to do this.
Put simply, solve the above 2 equations for $x$ and $y$.
Any help will be appreciated.
