I feel a major component that’s being missed here is friction. You can always push an object and you will feel an equal force back, but the friction you have with the ground can make it hard to notice this. For instance, if you try and push something while on ice, you will go backwards.
Also, to piggy back on the ball throwing example someone else gave, if you were floating in space and you threw a baseball, both you and the baseball would push off with an equal force, however, F=ma. If you are 100 times the mass of the ball, then 100*a1 = 1*a2, where your acceleration is a1 and the ball’s acceleration is a2. All equations aside, your acceleration is going to be 100 times less than the baseball because your mass is 100 times more.
Another example where you’ll notice this kickback more is while bowling, especially in socks. The bowling ball is closer to your mass, so you can feel its effects easier, even with friction.
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