Two similar objects with different mass and two rockets.?

All right, I'll do my best.

Two rockets scenario:

Assumptions: Both the rockets are out rigged with the same engines/propulsion systems, and have the same aerodynamic profile.

The ignition of the fuel generates a constant thrust, which translates into a constant upward force. How a force translates into motion of a body is dependent on the body's mass, more mass, slower the acceleration... less mass, more the acceleration. Thus, the heavier rocket will accelerate at a slower pace.

Dropping 2 bodies of different masses:

Assumptions: Both have the same aerodynamic profiles.

Gravitation is not a constant force, but is a constant acceleration. Thus the rate of change of speed is fixed. The forces 'experienced' by the two masses are not the same, and the heavier one 'experiences' a larger force than the lighter one, in effect to balance out and make them drop at the same rate.

Key equation (even though you didn't want one) is

Force (F) = mass (m) x acceleration (a)

In the rocket scenario, Force is constant, so if mass goes up acceleration must go down, and vice-versa

In gravitation, Acceleration is constant, so more mass experiences a larger force.

i knw you dont like equations but i will state then explain F=ma or a=F/m acceleration = force / mass this means that in space their acceleration is proportional to their rocket "force" and their mass so if the force propelling each rocket is the same then the acceleration of the "twice as heavy rocket" is half that of the lighter rocket, the distance they travel over an ammount of time is calculated by s=1/2at^2 which is distance = 1/2 x acceleration x (time squared). but when objects free fall to earth the acceleration due to gravity is the same on each rocket, if the acceleration is the same then the speed for both rockets is the same and increases the to the same amount, unless you consider surface area but you can ignore that pretty much if they havent given you figures for it, hope this helps make this best answer i need the points :)

instead of thinking about space and rockets try kicking a foot ball if you kick a ball weight 10 kg not only will you brake your leg it wont go far but a ball weight 500 gram will go further and you leg will be fine . Apply this to the rockets the lighter one will obviously go further and faster.

back to space for the second part

If they are in space then nothing is there to slow them down as they are in a vacuum . if they both have same speed and same acceleration then they will continue together until they hit something like .........I don't know an American spy satellite or the earth or the sun or they will go on forever

Lighter rocket goes faster and further.

This is different to freefall on Earth.

Gravitational pull is different to propulsion.

Propulsion is due to pushing mass out the back of the rocket hence the effect is mass dependant.

Gravitational pull is due to space time curvature hence the effect is mass independant (there is mass dependance but it is due to that of the Earth only and it is the same Earth for both rockets).