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   Author  Topic: Bus stop shade  (Read 193 times)
dudiobugtron
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Bus stop shade  
« on: Dec 19th, 2016, 10:18pm »
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Above some countries, such as the one this riddle is set in, there is a hole in the ozone layer. This means even a few minutes of direct exposure to sun (without protection) can cause radiation burns.
 
For this reason, our protagonist (dudio) likes to stay in the shade as much as possible.  Sometimes though, when waiting for a bus, the only shade available is from a small bus-stop sign, just large enough to protect dudio's head if he positions himself correctly. (So the sign is in a direct line between dudio's head and the sun.)  Since the sign is quite small, though, this can be difficult to do quickly.  A naive trial-and-error method, for example, might take a few minutes, somewhat defeating the purpose of searching for shade!
 
Part 1) What strategy does dudio use to easily position the sign in line with his head and the sun?
(PS: Extra credit if you come up with a strategy that works even better than dudio's!)
 
Part 2) One day, after using the above strategy, dudio found that the sign offered no protection at all from the sun! What mistake had dudio made?
« Last Edit: Dec 19th, 2016, 10:52pm by dudiobugtron » IP Logged
rloginunix
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Re: Bus stop shade   busstop.jpg
« Reply #1 on: Dec 20th, 2016, 8:00am »
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on Dec 19th, 2016, 10:18pm, dudiobugtron wrote:
(PS: Extra credit if you come up with a strategy that works even better than dudio's!)

Use an umbrella.
 
 
Barring weird sign pole/dudio height ratios and, within the given proportions, making a lot of simplifying assumptions (sun rays hitting the given arrangement are parallel, the sign is attached to a standalone "thin" pole, a right triangle is an acceptable mathematical model, etc.), one way to do that is as follows:
 
- facing the sign's shadow, put your back against the sign's pole
 
- walk the line shadow cast by the sign's pole until the centers of the shadows cast by your head and that of the sign coincide
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Grimbal
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Re: Bus stop shade  
« Reply #2 on: Dec 20th, 2016, 8:47am »
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on Dec 19th, 2016, 10:18pm, dudiobugtron wrote:
Part 1) What strategy does dudio use to easily position the sign in line with his head and the sun?

Look at the shdow of the sign B and the shadow of your head A.  The vector AB is exactly by how much you must move.
Assuming the ground is plane.
 
on Dec 19th, 2016, 10:18pm, dudiobugtron wrote:
PS: Extra credit if you come up with a strategy that works even better than dudio's!

Work at night.  As every vampire knows.
 
on Dec 19th, 2016, 10:18pm, dudiobugtron wrote:
Part 2) One day, after using the above strategy, dudio found that the sign offered no protection at all from the sun! What mistake had dudio made?

He went out at night.
Assuming "one day" refers to a 24-hour period.
« Last Edit: Dec 23rd, 2016, 5:40am by Grimbal » IP Logged
towr
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Re: Bus stop shade  
« Reply #3 on: Dec 20th, 2016, 10:16am »
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Quote:
Part 2) One day, after using the above strategy, dudio found that the sign offered no protection at all from the sun! What mistake had dudio made?
The higher the sun in the sky, the thinner the shadow of the sign. So it may not cover the whole head.
 
But if you're not bald, you can just turn your back to the sun.
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alien2
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Re: Bus stop shade  
« Reply #4 on: Dec 21st, 2016, 10:24am »
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Never attempt to pierce the tire of a bus with a knife. But if you do, you'll get a big shade thanks to the bus, thus you'll be completely safe from radiation burns.
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dudiobugtron
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Re: Bus stop shade  
« Reply #5 on: Dec 21st, 2016, 2:21pm »
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on Dec 20th, 2016, 10:16am, towr wrote:

The higher the sun in the sky, the thinner the shadow of the sign. So it may not cover the whole head.

Indeed!  This was not the mistake dudio made, but it was probably another mistake waiting to happen!!
 
Quote:
But if you're not bald, you can just turn your back to the sun.

This would work (even if bald) to protect dudio's face; unless of course the sun was high in the sky as above! Tongue
 
on Dec 20th, 2016, 8:00am, rloginunix wrote:

Use an umbrella.

Last time dudio tried that he left it on the bus! Wink
 
Quote:
- facing the sign's shadow, put your back against the sign's pole
 
- walk the line shadow cast by the sign's pole until the centers of the shadows cast by your head and that of the sign coincide

This is a good solution and it works, but this:
 
on Dec 20th, 2016, 8:47am, Grimbal wrote:

Look at the shdow of the sign B and the shadow of your head A.  The vector AB is exactly my how much you must move.
Assuming the ground is plane.

Is the one I was expecting.
 
Quote:
Work at night.  As every vampire knows.
This works to avoid the sun; however it also works to avoid the buses!  I guess vampires don't take public transport that often.
 
Quote:
He went out at night.
Assuming "one day" refers to a 24-hour period.

Not the answer I was expecting.
 
on Dec 21st, 2016, 10:24am, alien2 wrote:
Never attempt to pierce the tire of a bus with a knife.  

You sound like a man (or alien) speaking from experience!
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alien2
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Re: Bus stop shade  
« Reply #6 on: Dec 22nd, 2016, 10:47am »
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on Dec 21st, 2016, 2:21pm, dudiobugtron wrote:

You sound like a man (or alien) speaking from experience!

I may be many things, but I am not a hooligan. I am an alien, dammit! Which is worse? It depends on your point of view. W/o aliens, Sigourney would have no fame nor plenty.  
« Last Edit: Dec 22nd, 2016, 10:48am by alien2 » IP Logged


dudiobugtron
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Re: Bus stop shade  
« Reply #7 on: Dec 22nd, 2016, 1:43pm »
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I forgot to add that rloginunix was actually close to the expected answer for part 2 - although he may not have realised it at the time!
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