Projectile motion with air resistance

A small basketball is kicked. The path is plotted point by point in Logger Pro. Two complete trajectories are shown below. Neither is symmetrical.

Fitting a parabola to the first part of the curve gives an estimate of the path if there were no air resistance.

Plotting the horizontal velocity for both trajectories shows that air resistance reduces u_x by 50% over the time of flight in both cases. Plotting the vertical velocity shows a much smaller effect, because the small force due to air resistance is added to the much larger weight of the ball. The vertical acceleration is less than g, the free fall value of the acceleration due to gravity. This is not a reliable method for the determination of the acceleration due to gravity since the scale (marked on the goal posts) is a few meters behind the actual trajectories.

Suggestions for further work

• It would be interesting to compare the estimate of range without air resistance in graphs 1 and 2 with calculated trajectories based on the initial velocity components. [An overlay parabola is a more convenient way of making the figures for this type of estimate.]
• The launch velocity could be measured with a radar gun and compared with the initial velocity determined with the components from graphs 3 and 4.
• It would be interesting to plot the horizontal acceleration due to air resistance and to process that data to find the drag as a function of velocity.
• It might be possible to use a ball launched to develop a limited empirical model for the range and maximum height reduction due to air resistance with launch angle for a particular ball and launch velocity.
• ... or ....
• for a particular launch angle and different initial energies.