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Multidisciplinary
Design, Analysis, and
Optimization Branch
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EDUCATIONAL ACTIVITIES: THE NASA AEROQUIZ
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Week of 12/7/98:
Q:
Ground-based telescopes can rarely view an image with a resolution
better than about one arc-second. For this reason, no one has been able
to view the flags that Apollo astronauts left on the moon. The Hubble Space
Telescope, however, can resolve images about ten times smaller, or 0.1
arc-seconds. Assuming the Hubble could deal with the moon's glare, could
it see the flag at Tranquility Base?
A:
No. Using simple trigonometry, 0.1 arc-seconds at 240,000 miles is about
600 feet -- still not good enough to see the flags.
Congratulations to "glfras."
Week of 12/14/98:
First in a series of aerospace logic problems!
Q:
There are three closed hangars at the top secret Area 51 at Nellis
Air Force Base. One hangar contains Mach 10 spyplanes, another
contains alien flying saucers, and the other contains both
spyplanes and flying saucers. Each hangar has a sign. One sign
says "Spyplanes," another sign says "Saucers," and the other sign
says "Both." However, to confuse the onlookers peering through
high-powered telescopes who believe that the truth is indeed out
there, each hangar is labeled incorrectly. You happen to have three
remotely-controlled door openers, one for each hangar door. From
your position in the desert, and at great personal risk, you can open
the hangar doors. The doors only open wide enough to see one vehicle
inside before they are stopped and the alarms go off. Opening doors
takes time, and the more doors you open, the greater your odds are
of becoming Doberman lunchmeat. What is the fewest number of hangars
you need to see open to be able to accurately know their contents?
A:
One. If you open the hangar labeled "Both," that is.
Since it was stated that each hangar was labeled incorrectly, this
hangar will not contain both spyplanes and saucers. Suppose you saw
a spyplane through that door. Then that hangar would contain all spyplanes.
Now, what about the other two? The hangar labeled "Spyplanes" does not
contain spyplanes (since it's labeled wrong and because we now know which
hangar is the spyplane hangar), so it must contain saucers. And the
third hangar (incorrectly labeled "Saucers") must contain both saucers
and spyplanes.
Congratulations to Nicolas Cousineau.
Week of 12/21/98:
Second in a series of aerospace logic problems!
Q:
A pilot has just loaded his heavy cargo of legal briefs
onto his business jet. The clients, five lawyers in all, then board
the aircraft. The pilot becomes concerned that the heavy payload
will increase the required takeoff field length beyond that of the runway.
He has only a pocket ruler. His clients are impatient. Using only
the ruler, how can he quickly estimate the gross weight of the aircraft?
A:
The pilot could simply measure the approximate footprint on the ground
of each tire and multiply by the pressure of each tire.
Congratulations to Dick DeLombard.
Week of 12/28/98:
Third in a series of aerospace logic problems!
Q:
Every week, you board Shea D. Flyer's commuter airplane for your
connection to Hoboken. And every week, Shea offers a double-or-nothing
ticket price deal to a single passenger that he chooses at random.
Shea has the passenger draw one of two slips of paper from a hat.
One slip has "Double Fare" written on it, and the other, allegedly,
has "Free Ticket" written on it. Week after week, Shea collects a
double fare. You begin to suspect that Shea is cheating and that
both slips of paper say "Double Fare." This week, Shea chooses you.
You decide to play his game. You can't pull both slips out and expose
Shea as a cheat, because that would be impolite. And you're awful at
sleight-of-hand, so you don't try anything like that, either. But
you win a free fare. How?
A:
Congratulations to Vatsala Kamath for suggesting
that you could just draw a slip, look at it to make sure it says "Double Fare,"
declare that you've won, and then eat the slip! If challenged, you could
just tell people to look at the other slip! And congratulations to
Ed Winchester for suggesting that you bet Shea
double or nothing that you will pick the one that says "Double Fare."
In front of all the people, he might not back out of the challenge and
you would win.
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