What happens if a body free-falls at a certain speed? It is known that a body falling to the ground is affected by gravity, and its velocity increases by 9.8 m/s per second.
But when this body is falling, and it reaches the speed of 340 m/s (the speed of sound as a limit example), So its velocity will keep increasing to larger than the velocity of sound?
If so it increases, and it reaches a velocity of half the speed of light, then we know that the mass of this body would increase as it's moving, and this increase in mass will not affect the velocity as we know. but if this mass keeps increasing, and velocity keeps increasing by 9.8 m/s/s. Special relativity predicts that it's impossible for objects that have mass to reach the speed of light. so this body will not continue its increase in speed and mass. so there must be a velocity and mass limit for this body. Or else this body's mass will be larger than the mass of the planet itself. and make a curvature in space-time fabric larger than that of the planet.
So There have to be a relation between the velocity of this body, It's mass, the mass of the planet, and the relative velocity of the rotation of the planet, so we can conclude the speed limit that this body cannot exceed from them.
 A: A free-falling body will not approach anywhere near half the speed of light due to gravitational pull at the earth's surface, so the second part of the question (involving relativistic effects) is sort of nonsensical.
As for the first part, one can get a very rough approximation of whether a body can even approach the transonic regime (Mach 0.85-1.2) using the free-fall modified drag equation,
$$v=\sqrt{\frac{2g m}{A C_D \rho }}$$
where $\rho,C_D,A,g,m$ are the air density, drag coefficient, projected area, gravitational acceleration and object mass respectively. If $v\ll v_s$ where $v_s$ is the speed of sound, it is unlikely that the object will approach the transonic region, simply due to the fact that its terminal velocity is limited by drag friction.
This has a an intuitively obvious visual interpretation in terms of the size of the object, namely that dense objects with small surface area will have a better chance of breaking the sound barrier than light objects with large surface area. Additionally, letting the size of an object be sized by a length scale parameter $\lambda$, one also observes that the terminal velocity $v$ transforms under an increase in object size as
$$v\rightarrow \sqrt{\frac{2g \left(\lambda^3m\right)}{\left(\lambda^2A\right) C_D \rho }}=\sqrt\lambda v$$
which should also seem visually sensible.
If $v>v_s$, wave drag forces will need to be considered to determine if it's possible for the object to break the sound barrier, and in general there is a several-fold increase in drag at the transonic boundary which will need to be overcome.
