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Vertical motion

Graphical representation of our solution

Height y(t) of the plastic ball as a function of the time t/T. α = vterm		Velocity v(t) of the plastic ball as a function of the time t/T. α = vterm

In the above figures we represent graphically the motion of the plastic ball as it is given by our solution for the dynamical equation of objects moving vertically in air. The horizontal axes of the figures are in the dimensionless quantity t/T. The height is given in units v_termT which has the dimension of length. The velocity is given in units v_term which has the dimension of m/s.

In the lefthand-side figure we show how the height varies with time. The figure sets out at t/T≅-1.5. At first the plastic ball rises fast in time, but then it slows down untill it reaches its maximum position. From thereon the plastic ball starts falling towards the Earth thereby reducing its height. But, instead of doing so with increasing velocity as does the solid metal ball, the plastic ball reaches its terminal velocity somewhere near t/T=2 and starts moving with a constant velocity, in which case the height decreases linearly with time (straight line) instead of quadratically (parabolic curve) as for the solid metal ball. Only near the maximum height the curve is approximately equal to a parabolic curve. That phenomenon was discussed in a previous page.

In the righthand-side figure we show how the velocity varies with time. That curve shows even better the difference with a vertically moving object that does not suffer from air resistance. For the latter type of objects the corresponding curve is given by a straight line. Here the straight part, which runs from t/T≅-0.5 to t/T≅+0.5, occurs only near the maximum height of the plastic ball where the velocity is small and hence the air resistance negligible. From about t/T=2 on the velocity turns even constant and equal to -v_term.

viscosity