A high-speed test of the equivalence principle

It is well known that Newton’s work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different mass that are simultaneously released from rest and allowed to fall under the influence of gravity through a vacuum should hit the ground at the same time (this is essentially what is called the equivalence principle in general relativity). In popular legend, it is said that Galileo tested this by dropping two balls of different masses from the Leaning Tower of Pisa and showing that they hit the ground at the same time, but the historical evidence suggests that this is unlikely as he seems to have experimented mostly with balls rolling down inclined slopes