I understand the goal but given the code listed, haven't you already achieved it? For any set of measurements and landing points you can already calculate/estimate k and m.

If you you have multiple sets measurements and landing points that result from the same "true" values of k and m, then you could apply your code as a function, obtain the multiple estimates of k and m and even calculate measures of precision. (With the measures of precision associated with how you obtain multiple sets of measurements and landing points.)

If the multiple sets of measurements and landing points are from different "true" values of k and m, then you could try to estimate k and m using a simpler function of the measurements (using NonlinearModelFit). But you also need to specify the error structure of the measurements and landing points - i.e., how the experimental data is generated. Is there a single projectile? Or multiple projectiles with different masses and/or drag constants? How is the start speed varied among runs of the experiment?

And, finally (almost done with the sermon), the variability of the estimates might very well differ depending on the projectile's properties (lighter projectiles might have more variability than heavier projectiles, for example). It's not clear to me that NonlinearFit allows much flexibility in setting the covariance structure.