Felix Baumgartner dive (14 October, 2012)

Graphical representation of our solution

Height of a solid ball of 128 cm diameter and 120 kg mass as a function of the time at intervals of 1 second.		Velocity of a solid ball of 128 cm diameter and 120 kg mass as a function of the time at intervals of 1 second and actual data (dots).

In the above figures we represent graphically the motion of a solid ball of 128 cm diameter and 120 kg mass as it is given by our solution for the dynamical equation of objects moving freely and vertically in air under the influence of the gravitational attraction near the surface of the Earth.

In the lefthand-side figure we show how the height varies with time. The figure sets out at t=0 seconds where the height of the ball, initially at rest, equals 39 km.

In the righthand-side figure we show how the velocity varies with time and compare it to the data (dots) obtained from the video.

At first the solid ball does not notice the air resistance and falls freely with increasing velocity, thereby reducing its height. The quadratic time dependence results in a parabolic curve in the height-time graph for the motion of solid ball. This lasts untill about t=50 seconds, where the ball exceeds the velocity of sound. Then the air resistance becomes noticeable because the velocity starts slowing down. The velocity would eventually become constant, the terminal velocity, but that it still not visible in the graph.