Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses.

If only the force of gravity acts on the ball, the mechanical energy will be conserved during its flight.

More specifically, if the ball is bounced at an angle θ with the ground, the motion in the x- and y-axes (representing horizontal and vertical motion, respectively) is described by[6] The equations imply that the maximum height (H) and range (R) and time of flight (T) of a ball bouncing on a flat surface are given by[2][6] Further refinements to the motion of the ball can be made by taking into account air resistance (and related effects such as drag and wind), the Magnus effect, and buoyancy.

Drag will cause the ball to lose mechanical energy during its flight, and will reduce its range and height, while crosswinds will deflect it from its original path.

The lift coefficient is a complex factor which depends amongst other things on the ratio rω/v, the Reynolds number, and surface roughness.

[4][13][14] In sports like tennis or volleyball, the player can use the Magnus effect to control the ball's trajectory (e.g. via topspin or backspin) during flight.

In golf, the effect is responsible for slicing and hooking which are usually a detriment to the golfer, but also helps with increasing the range of a drive and other shots.

[17] Ball tampering is often illegal, and is often at the centre of cricket controversies such as the one between England and Pakistan in August 2006.

[20] According to Archimedes' principle, this buoyant force is equal to the weight of the fluid displaced by the object.

This energy loss is usually characterized (indirectly) through the coefficient of restitution (or COR, denoted e):[23][note 1] where vf and vi are the final and initial velocities of the ball, and uf and ui are the final and initial velocities of the impacting surface, respectively.

In the specific case where a ball impacts on an immovable surface, the COR simplifies to For a ball dropped against a floor, the COR will therefore vary between 0 (no bounce, total loss of energy) and 1 (perfectly bouncy, no energy loss).

These are especially of interest when the ball impacts the surface at an oblique angle, or when rotation is involved.

Likewise, the energy loss at impact can be related to the COR by The COR of a ball can be affected by several things, mainly External conditions such as temperature can change the properties of the impacting surface or of the ball, making them either more flexible or more rigid.

[22] In general, the ball will deform more at higher impact velocities and will accordingly lose more of its energy, decreasing its COR.

Similarly, in cricket, there are various methods of spin bowling that can make the ball deviate significantly off the pitch.

[36][37] Assuming perfectly elastic collisions, the basketball impacting the floor at 1 m/s would rebound at 1 m/s.

[note 2] In reality, due to inelastic collisions, the tennis ball will increase its velocity and rebound height by a smaller factor, but still will bounce faster and higher than it would have on its own.

[37] While the assumptions of separate impacts is not actually valid (the balls remain in close contact with each other during most of the impact), this model will nonetheless reproduce experimental results with good agreement,[37] and is often used to understand more complex phenomena such as the core collapse of supernovae,[36] or gravitational slingshot manoeuvres.

[39] Several sports governing bodies regulate the bounciness of a ball through various ways, some direct, some indirect.