Indian teenager finds closed-form equations for projectile motion *with* air resistance.

[mackys]

300 years ago, Newton posed the problem of finding a closed form equation to model the motion of a projectile acting under the influence of both gravity and air friction. He couldn't solve it, and until recently nobody knew if there was an equation that did describe it

Comments

[a_gs]

The solution doesn't solve x(t) and y(t) with given x(t0), y(t0), x'(t0), y'(t0), it only establishes relationship between components of velocity vector. Or, as our friends from /b/ would say, differential equation is differential, if our friends from /b/ were talking about differential equations. It might be helpful to reduce the number of operations while performing approximate calculations by iterations (calculate one component the usual way, get another with this, plug the result into the next iteration) but then there is a question of precision and how errors will accumulate compared to both components being calculated with the same procedure.