Final answer:
When ignoring air resistance, both a 4.0-kilogram rock and a 1.0-kilogram stone in free fall will have the same speed after falling for 2.0 seconds, as the acceleration due to gravity is constant. The ratio of their speeds will be 1:1.
Step-by-step explanation:
The question pertains to the concept of free fall in physics and the effect of gravity on objects with different masses. According to the laws of motion and gravity, when objects are in free fall, the acceleration due to gravity is constant, approximately 9.8 m/s2, and mass does not influence the rate of fall assuming no air resistance. Thus, after 2.0 seconds of free fall from rest, both the 4.0-kilogram rock and the 1.0-kilogram stone would have the same speed because the acceleration due to gravity is the same for all objects regardless of their mass.
Using the formula v = gt, where v is the final velocity (speed), g is the acceleration due to gravity (9.8 m/s2), and t is the time, we find that:
v = 9.8 m/s2×2.0 s = 19.6 m/s
Therefore, the ratio of the rock's speed to the stone's speed after falling for 2 seconds is 1:1, since both velocities are 19.6 m/s.