Answer 1:
Newton's third law does apply here, but it is
sometimes hard to conceptualize. The forces are
equal and opposite, but apply to different bodies.
If they applied to the same body, nothing would
move. Think of pushing a box. At each
interface, there are equal forces in each
direction. So think about the side you're
pushing. There is force on the box you are
pushing, and a force backwards on you from your
hands. Similarly, you are pushing off of the
Earth, so there is a force forward on you, and
backward on the Earth. So, the forces on you
cancel, the box moves forward, and the force on
the Earth is infinitely small compared to the size
of the Earth. Does this help? I can draw and send
you a diagram of the situation if that would help,
just send another email. :)
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