**Published on** November 25th, 2012 |
*by Simi*

# Mathematics of the mission to the edge of space

On the 14th of October space diver Felix Baumgartner became the first person to exceed the sound barrier without any engine assistance.

Descent data:

*Exit altitude: 39,045m above sea level
*

*Total jump duration: 9 minutes 3 seconds*

*Freefall time: 4 minutes 20 seconds*

*Freefall distance: 36,529m*

*Altitude at landing point: 1,363m above sea level*

*Maximum speed: 1,342.8km/h (Mach 1.24) after 42 seconds of descent*

Provide numerical answers correct to two decimal places for the following.

**a)** What were his average speeds of descent (in m/s) during and after freefall (i.e. before and after parachute)?

**b)** If we assume his speed of descent increased from zero to the maximum level linearly, what was his acceleration in m/s^{2}? How does this compare with the standard acceleration due to gravity at the earth’s surface (9.81 m/s^{2})?

**c)** With the above constant-acceleration assumption, how far had he descended after 42 seconds?

Extension question: Draw a speed vs time graph to model Baumgartner’s descent ensuring that the area under the graph up to a point in time represents the distance fallen up to that time.

Question created by Chaitanya Rao, Daniel Mathews, Norman Do

Image courtesy of RedBull STRATOS

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