I am confused about Newton's 3rd Law. If a person jumps off the ground a force is applied both to the person and to the ground. However, as $F=ma$ acceleration experienced by the Earth is much less than that experienced by the person.
But: I press with gravitation force on the ground so it should press with the same force on me, so if my mass is less than earth mass my acceleration should be greater as well but I am not moving (flying)?
Second: If small rocket(with small mass) pressure against bigger rock with greater mass the rocket should have greater acceleration towards direction opposite to its flying path so how the rocket can actually move the rock(towards left at picture where rock acceleration is small) and not the opposite(rocket acceleration at picture towards right is bigger)?
Edited
If a rocket with mass $m_{rocket}$ pushes against a rock with mass $m_{rock}$ with force $F_{thrust}$ the rock will push back with equal force (Newton's 3rd Law). The rocket will experience an acceleration $a_{rocket}$ in the opposite direction of $F_{thrust}$ and the rock will experience $a_{rock}$ in the same direction as the thrust. However, in this example $m_{rocket} < m_{rock} \therefore a_{rocket} < a_{rock}$
Why doesn't the rocket move in the opposite direction of $F_{thrust}$ since the rock has a greater mass?
Not sure if it helps but added picture to second question
Edit:To put second question simple how a small(low mass) object can push big(great mass) object if according to newton 3rd law a big mass object causes greater acceleration on small mass object
Best Answer
To the first question: Newton's third law states that every force has an equal and opposite force. Thus, the force that Earth exerts on you with gravity (a big mass causing a huge acceleration on a small mass) is countered exactly by the normal force of the ground (again, a big mass causeing a huge acceleration on a small mass, but this time in the opposite direction). You can see this when you jump, and the normal force is no longer applied to your body, you quickly fall to Earth. In a sense, the force the ground pushes back on you is really equal and opposite to the gravity of the Earth pulling on you.
I'm not sure I understand your second question. It doesn't really specific the situation well, and it's poorly worded; if you rephrase it I can hopefully give you answer.