I experimented heavily with this image and am for the most part happy with the results. This is 100% Paint Tool SAI. Hopefully I can tighten up the technique and bring about better results with the next image.
> calculate the correct trajectory to set that sling at
STAND ASIDE, SCRUBS I GOT THIS
1) Let x and y be on an imaginary plane, such that the slingshot is coincident with both this plane and with the y-axis, and such that Rainbow Dash and the launch point both lie on this plane. The origin (0,0) will be at the launch point, and the positive x-axis will point toward RD and be parallel to the ground.
2) Assuming the slingshot behaves as an ideal linear spring, and assuming we know both the elastic's stiffness (k, in N/m) and Pinkie's mass (m, in kg), find the initial launch speed (v, in m/s) by relating it to "distance stretched back" via spring energy transferring to kinetic energy: PE = KE --> 0.5*kx2 = 0.5*mv2, v>0 .
3) Several boring rearrangements of various projectile motion equations gives us this equation. Assuming we know Dash's x-y coordinates relative to the origin (i.e. her distance from and height above the launch point), and assuming g = -9.81 N/kg, we can find the correct trajectory (i.e. angle θ) to launch Pinkie at.