Any projectile launched from Earth is slowed by interaction with the atmosphere. Most of this interaction is caused by friction. If we can talk about launching without worrying about the drag caused by friction, the discussion is easier. We can use the idea of conservation of energy to discover the velocity needed to escape the Earth's gravitational pull.

If the energy of motion (kinetic energy) of a projectile just equals the pull of gravitational (potential) energy, the projectile can barely escape the Earth.

m v2  =  G M m
2 r

Where:   m = projectile mass (in kg)
   v = velocity (in km/s)
   r = radius of Earth (in km) = 6378 km
   M = Mass of Earth (in kg) = 5.96 X 1024 kg
 
G = Gravitational Constant = 6.67 10-11   m 3
kg sec2

Notice that the mass of the projectile can cancel on both sides of the equation. This is why the escape velocity is independent of the mass of the projectile.

v2   =  2 G M
r

Both a pebble and a rocket must each obtain an escape velocity of 11.2 km/s to escape the Earth.

Obviously it would require more force to accelerate the rocket to this velocity than the pebble, but, having reached the velocity, both could escape the Earth's gravitational field.