The flight of a golf ball

A skilled golfer hitting a drive can accelerate his club head from zero to 120 miles per hour in the quarter of a second before making contact with the ball. As a result, the ball leaves the tee with a typical speed of 175 miles per hour and at an angle of 11◦ to the ground. From that moment the golfer no longer exercises control. The trajectory of the ball is determined by the laws of physics. In elementary calculus we learn to model the trajectory of an object under the influence of gravity. The horizontal component of its velocity is constant, while it experiences a vertical acceleration down towards earth at 32.2 feet per second per second. This results in a parabolic trajectory which can be described exactly. Over a flat course a ball traveling with the initial speed and launch angle mentioned above would return to earth at a point 256 yards from the tee. In fact, observation of golf ball trajectories reveals that there shape is far from parabolic, as illustrated in Figure 1, and that golfers often drive the ball significantly higher and farther than the simple formulas from calculus predict, even on a windless day. The discrepancy can be attributed to the fact that these formulas assume that gravity is the only force acting on the ball during its flight. They neglect the forces that the atmosphere exerts on the ball passing through it. Surprisingly, this air resistance can help to increase the range of the ball.