Given someone does a "regular" push on an object, what determines how much force it exerts? For a long time I assumed that (discounting metal content, allomantic strength, ect) the force a push exerts is solely based on the inverse square law; that is to say it gets weaker as the separation increases exactly like gravity or the electrostatic forces.
However, there are a few lines in the series that suggest it's also based on the relative velocity of the Pushee and Pusher. When Vin Pushes on a coin horizontally, the recoil is barely strong enough to make her change her stance. However, the moment the coin hits a wall, it sends her flying. This suggests that objects moving away from an Allomacer are pushed on with less force than a stationary object.
In Shadows of Self, Wax has to use quite a few pushes in order to get to the top of ZoBell tower, leading him to use the grappling hook. However, on his exit, he is able to jump out and land by pushing on a single object on the ground. Physics tells us that the energy needed to lift an object to a certain distance is the same amount of energy needed to completely stop that object after falling that same distance. If the force was the same going up and going down, that single push would have only nullified a few stories of falling. My theory is that because he was falling, and therefore going towards the coin(or was it a bullet?) his push was much stronger than when rising.
This has interesting implications for weaponized coins. Bullets, slings, and bows are dangerous because of the kinetic energy that was imparted onto them before contact. Shot coins however would be more like a stabbing spear; the initial speed is good and all, but what really matters is how hard you're pushing while going through the target.