Many people know that Apollo 14 astronaut Alan Shepherd hit a golf ball on the moon. In so doing, he became the first person to ever play golf on another world. Having hit the golf ball in the moon's low gravity environment, the ball likely remained above the surface for more than a minute. During that time, the ball might have traveled more than two miles. Nobody actually calculated the precise distance the ball traveled. Physicists have estimated the ball's traveling distance based on their knowledge of the environment and by making assumptions about the force Shepherd applied to the ball on impact and the angle with which he struck it. They estimate it might have landed between two and two and a half miles from the impact point. Text book physics problems provide one with all the information required to solve the problems. In real life situations, much of the information is unknown and therefore answers are predicated on mis-informed presumptions. We cannot truly know precisely how far Shepherd's ball traveled. However, he undoubtedly holds the record for the longest drive in history, far surpassing Mike Austin's highly impressive world record 515 yard drive.*
One can make a golf ball travel for quite a distance on the moon for two reasons. First, the moon's gravity is only one sixth as strong as Earth's. So if you strike a golf ball up at an angle, it will describe a parabolic arc ascending to a high point, at which its vertical velocity is momentarily zero, and then descending back down to the surface. On Earth, a golf ball doesn't remain in the air for long as the planet's gravity quickly pulls it back down. On the moon, a golf ball will travel much farther because the comparatively weak surface gravity will accelerate it back to the surface more slowly. During that time, the ball travels with a constant horizontal velocity, at least in theory.
On Earth, however, air resistance impedes the ball's travel. As this resistance is proportional to the velocity squared, the faster a ball moves, the greater the impeding resistance becomes. The second reason a golf ball travels farther on the moon is its lack of atmosphere. There is no air resistance on the moon to slow the ball's travel. The faster one hits a golf ball, the farther it moves as no fluid resists it.
As for making a ball leaving the moon altogether, well, a human truly couldn't. The moon's gravity is weaker than Earth's, but still quite strong. The moon's escape velocity is about 5,310 miles per hour! In order to escape its gravity field, an object would have to at least move at this velocity. Not even the strongest human could launch a golf ball at such a speed. One can make a golf ball travel for a couple miles on the moon, but the ball would always end up landing back on its surface.