Cannonball Competition
by Kevin J. Lin
With a little bit physics and math you can lay claim to that $1,000,000.
The correct order of arrival is as follows:
#4 is the first to arrive. Without air resistance, he would arrive in
about 14 seconds. Is the air resistance enough to allow the moon divers
to pass him? Probably not, air resistance rises with velocity and this
diver won't be anywhere near his terminal
velocity of 300m/s when he hits the water.
#1 comes in second. His condition is the same as #4's but at a cooler
temperature. Cooler air is denser, so more air resistance.
#5 comes in third. The moon's gravity is much weaker than the Earth's,
so doesn't catch up with his terrestrial competitors even though he doesn't
have to overcome air resistance. And of course, his parachute does nothing
without an atmosphere. He lands about 35 seconds after jumping (gravity
increases slightly as he descends, but not by much).
#3 comes in fourth. Again, the water temperature difference mean he trails
#5 by a slight margin, almost certainly less than half a second later.
#2 comes in fifth. We don't specify the kind of parachute, but assuming
it's one that slows the diver to a "safe" speed, he can't be
moving more than a few meters per second. Even at 10 m/s, he'll come in
over a minute later.
#6 and #7 tie for last, by failing to reach the bottom of the pool.
#6 hits a massive block of ice with a bang (water is a solid at 25°
F). #7 has a lot more mass than his competitors, but also a lot less density.
In fact, he floats.
With these results, you can collect the $1 million jackpot. If inflation
between now and then averaged 2.5% per year, this sum would have a pre-tax
value of over two dollars in today's money.