On October 14, 2012, Felix Baumgartner became the first human being to break the soundbarrier while falling freely. He jumped from a capsule that was lofted by a balloon to analtitude of 127,852 ft (38.96 km). The speed of sound at that altitude is 690 mi/h.(a) Assuming that air friction (drag) is negligible at such altitudes, how far would he haveto fall to reach the speed of sound? (The approximation for the gravitational potentialenergy near the Earth’s surface, Ug ≈ mgy, is accurate to better than 1% even at suchaltitudes. Track units carefully, though!). Draw energy bar charts of your system atthe start of Felix’s jump and when he reaches the speed of sound to support youranswer.(b) Friction is not negligible, even at this altitude. Baumgartner actually reached thespeed of sound at an altitude of 109,731 ft (33.45 km). What fraction of the system’schange in gravitational energy was converted to thermal energy (mostly thermal energyin the air) by the time Baumgartner reached the speed of sound? Again, draw energybar charts of your system at the start of Felix’s jump and when he reaches the speedof sound to support your answer.
On October 14, 2012, Felix Baumgartner became the first human being to break the sound
barrier while falling freely. He jumped from a capsule that was lofted by a balloon to an
altitude of 127,852 ft (38.96 km). The speed of sound at that altitude is 690 mi/h.
(a) Assuming that air friction (drag) is negligible at such altitudes, how far would he have
to fall to reach the speed of sound? (The approximation for the gravitational potential
energy near the Earth’s surface, Ug ≈ mgy, is accurate to better than 1% even at such
altitudes. Track units carefully, though!). Draw energy bar charts of your system at
the start of Felix’s jump and when he reaches the speed of sound to support your
answer.
(b) Friction is not negligible, even at this altitude. Baumgartner actually reached the
speed of sound at an altitude of 109,731 ft (33.45 km). What fraction of the system’s
change in gravitational energy was converted to thermal energy (mostly thermal energy
in the air) by the time Baumgartner reached the speed of sound? Again, draw energy
bar charts of your system at the start of Felix’s jump and when he reaches the speed
of sound to support your answer.
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