In the case of a ball and a feather in free fall in a vacuum, they both fall at the same rate. This phenomenon is known as Galilean relativity or equivalence principle, which states that if two objects are dropped at the same time in the same gravitational field, they will accelerate at the same rate.

This was famously demonstrated by Galileo in his experiment dropping two balls of different masses from the leaning tower of Pisa, showing that both hit the ground at the same time.

Thus, in the absence of air resistance, both the feather and the ball would reach the ground at the same time in a vacuum.