The terminal speed of a ping-pong ball is about \(20 \mathrm{mph}\). From the top of a tall building on a windless day, a ping-pong ball is thrown downward with an initial speed of \(50 \mathrm{mph}\). Describe what happens to the ball's speed as it moves downward from the moment it is thrown to the moment when it hits the ground.

Understanding forces is crucial to analyzing motion in physics. Force, in its simplest definition, is a push or a pull on an object that can cause it to accelerate. Forces can act through direct contact or at a distance, as with gravity.

When examining an object such as a thrown ping-pong ball, identifying all the forces acting upon it is the first course of action. In this scenario, the primary forces are gravity, pulling the ball towards Earth, and air resistance, which opposes the ball's motion through the air. Newton's second law, expressed as \( F = ma \) (force equals mass times acceleration), forms the basis for analyzing the effects of these forces on the ball. By calculating the net force acting on the ping-pong ball and considering its mass, we can determine its acceleration or deceleration at any point during its fall.

Acceleration due to gravity, often symbolized as \( g \) and approximately \( 9.81 \text{ m/s}^2 \) on Earth, is the constant rate at which all objects, regardless of their mass, are pulled towards the planet's surface.

For a ping-pong ball thrown downward, gravity exerts a force that would increase its velocity by \( 9.81 \text{ m/s}^2 \) each second if it weren't for the counteracting force of air resistance. This is to say, in a vacuum, any object would continue to accelerate as it falls. However, within Earth's atmosphere, other forces come into play that alter this acceleration, specifically air resistance which is encountered by the ball immediately after it is thrown.

Air resistance is a form of friction that occurs between the surface of a falling object and the air particles it encounters. This force increases with the speed of the object and, more precisely, is proportional to the square of its velocity.

As the ping-pong ball accelerates due to gravity, it also speeds up, making the air resistance grow. Once the force of air resistance equals the force of gravity, it results in a net force of zero, and the ball no longer accelerates -- this is when it reaches terminal speed. Terminal speed is when the object moves at a constant rate without further acceleration. Conclusively, the ping-pong ball will continue to move at or decelerate towards its terminal velocity of 20 mph, balanced by the two opposing forces. This illustrates the dynamic relationship between gravitational pull and air resistance experienced by objects in motion.