Usually, in most physics engines that are out there, the way that collisions are solved is by applying some impulse to both colliding bodies.
While I understand that impulses are just force that is already integrated into time, and will result into velocity added at the end of the frame, why not simply project both bodies out of collision and removing their velocity component that is going towards the collision?
I'm not really sure, but it really looks like classic platformers only stopped the character instead of adding impulse to it. Is this right?
And if yes, why the added complexity of using impulses in modern engines?