As stated, the event permits calculation of Δ(mV) of a basketball. Our path of thought is not completed here.

Chest PassA manner of practicing the basketball "chest pass" is to make crisp throws of the ball into a spot on the wall of the gym. The mass of a basketball is about 0.6 kilograms and its speed toward the wall and on rebound are estimated to be 12 and 10 meters per second, respectively. The figure shows the velocities of the ball before (1) and after impact (2).

Newton's Second Law applies to this event. We write the law (basketball as system) then integrate it, showing all steps.

Variables are separated and the integration symbols are applied.

The momentum change of the basketball (left of equality) integrates readily. We apply cartesian coordinates with the usual I, K basis and evaluate it.

We have mathematically advanced our momentum equation through the easy integration of an exact vector differential of momentum (left of equality). But terms right of equality represent integration of the sum of all forces exerted on the basketball (integrand), over the differential time, the duration of the event. To procede, lets apply our knowledge of how a ball bounces. The "bounce" begins when the ball contacts the wall.

There We assuming the wall to be rigid. Upon contact, the ball if viewed as part of as surroundwall of what happens when a ball bounces. Specifically By our knowledge of how a basketball Since we know Lacking information, that integration cannot advanced explicitly. However, an implicit simplification is possible. When the mean value theorem of calculus (MVT) is applied to the integral, we obtain:

The MVT casts the recalcitrant integral as two parts which are the vector "average force" of the event and its scalthe duration of its effect, Δt. In this immediate sense, "average force" is a time average. Lets presume we know the duration time of the bounce event. Let it be denoted as some number Δt^*.