Could you please check my answers? Thanks!

1. You push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn’t this mean the forces cancel one another, making acceleration impossible? Why or why not?

-No, because in order to accelerate the car, you have to have that interaction between you and the car.

2. If you stand next to a wall on a frictionless skateboard and push the wall with a force of 30N, how hard does the wall push on you? If your mass is 60 kg, what is your acceleration?

30 N

a=f/a
a=60kg/30 N = 2 kg/n

3. When a rocket engine is above the Earth’s atmosphere, what does it push on to cause acceleration?

-The rocket engine when above the Earth’s atmosphere the rocket pushes on Earth’s atmosphere in order to accelerate.

5. A truck has a trailer attached. As the truck drives off it exerts a force on the trailer that tends to pull the trailer along. But, according to Newton's 3rd Law, the trailer exerts an equal and opposite force on the truck which tends to stop the truck. How, then, can the truck and trailer accelerate and drive off?

-The forces cancel out.

On number one, the answer is no,but the reason you gave is wrong. The force pushing back on your hand is equal to the friction on the car plus mass*acceleration.

2.3 are wrong.
5 I don't agree that the pull back force tends to stop the truck at all. Think some more on it.

1. In the scenario of pushing a heavy car by hand, the forces between you and the car do not cancel each other out. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When you push the car, you exert a force on it, and as a result, the car exerts an equal but opposite force on you. This force is what allows the car to accelerate. So, the forces do not cancel each other out, but rather create an interaction that enables the car to move.

2. If you push a wall with a force of 30N, the wall pushes back on you with an equal force of 30N. This is again explained by Newton's third law. However, in this scenario, your acceleration cannot be determined solely based on the force you exert on the wall. Acceleration is calculated using Newton's second law, which states the relationship between force, mass, and acceleration: F = ma. In this case, the force you apply is 30N, and your mass is 60 kg. To calculate your acceleration, divide the force (30N) by the mass (60 kg), so your acceleration would be 0.5 m/s^2.

3. When a rocket engine is above the Earth's atmosphere, it cannot push against the atmosphere to cause acceleration. Instead, rockets operate on the principle of action and reaction described by Newton's third law. Rockets carry their own fuel and exhaust gases, which they expel at high speeds in the opposite direction. So, the rocket engine pushes out exhaust gases with considerable force, and according to Newton's third law, this action generates an equal and opposite reaction, propelling the rocket forward.

4. In the example of a truck with a trailer attached, it is correct that according to Newton's third law of motion, the truck exerts a force on the trailer, and the trailer exerts an equal but opposite force on the truck. However, the forces between the truck and the trailer do not cancel each other out completely. The key aspect to consider is the distinction between the forces acting on the truck and the trailer separately, rather than focusing on the interaction between them. When the truck exerts a force to pull the trailer along, there is also a force of friction between the truck's wheels and the ground. This frictional force allows the wheels to grip the ground and propel the truck forward, overcoming the opposing force exerted by the trailer. So, it is the force of friction between the truck's wheels and the ground that enables both the truck and trailer to accelerate and drive off.