Silly Math Problems

[Jephph]

Here are a couple of math questions I've thought up, and wondered about.

#1
If you were to walk around a perfect sphere, would you be going uphill, downhill, neither, or both?

#2
Two identical cars are driving in the rain. Car A accelerates from 60-70mph at a constant rate for 10 seconds. Car B drives at a constant rate of 65mph for 10 seconds. Which windshield will be hit the most times with rain drops (assuming the rain falls at the same rate, same pattern, etc. for both cars)

 

[fatpat268]

#1 Neither

#2 No idea

 

[CraKaJaX]

Originally posted by: Jephph
Here are a couple of math questions I've thought up, and wondered about.

#1
If you were to walk around a perfect sphere, would you be going uphill, downhill, neither, or both?

#2
Two identical cars are driving in the rain. Car A accelerates from 60-70mph at a constant rate for 10 seconds. Car B drives at a constant rate of 65mph for 10 seconds. Which windshield will be hit the most times with rain drops (assuming the rain falls at the same rate, same pattern, etc. for both cars)

#1, I would say they would cancel each other out if it's a perfect sphere. So neither.

#2, speed doesn't have anything to do with it. I would say it would be the size of the windshield and how fast the rain is coming down...

 

[nakedfrog]

42 and potatoes.

 

[tefleming]

Originally posted by: Jephph
Here are a couple of math questions I've thought up, and wondered about.

#1
If you were to walk around a perfect sphere, would you be going uphill, downhill, neither, or both?

Neither. Perfect sphere = flat (hills would be "imperfections")

#2
Two identical cars are driving in the rain. Car A accelerates from 60-70mph at a constant rate for 10 seconds. Car B drives at a constant rate of 65mph for 10 seconds. Which windshield will be hit the most times with rain drops (assuming the rain falls at the same rate, same pattern, etc. for both cars)

Same (average speed + same time)


//edit :

#2, speed doesn't have anything to do with it. I would say it would be the size of the windshield and how fast the rain is coming down...

true...

 

[TuxDave]

Um.... so where's the math again?

 

[Atomic Playboy]

#1 Up and down are just our perceptions based on gravity. If we assume the sphere is the source of the gravity, then we will not feel we are moving up or down, but simply forward (similar to walking across the giant sphere we currently live on). If the sphere is not the source of gravity, then any perception of up or down will come from whatever the source of gravity is. If you were in a weightless environment, and the sphere were small enough that its gravitational effect on you were imperceptable, you would not feel as though you were moving up or down; it'd be more of a floating sensation.

 

[Jephph]

Originally posted by: CraKaJaX

Originally posted by: Jephph


#2, speed doesn't have anything to do with it. I would say it would be the size of the windshield and how fast the rain is coming down...

Hence the disclaimer of identical cars and the rain coming down at the same rate, same pattern, etc.

 

[Jephph]

Originally posted by: Atomic Playboy
#1 Up and down are just our perceptions based on gravity. If we assume the sphere is the source of the gravity, then we will not feel we are moving up or down, but simply forward (similar to walking across the giant sphere we currently live on). If the sphere is not the source of gravity, then any perception of up or down will come from whatever the source of gravity is. If you were in a weightless environment, and the sphere were small enough that its gravitational effect on you were imperceptable, you would not feel as though you were moving up or down; it'd be more of a floating sensation.

Fun fun. So if we get rid of the gravity aspect, it would be just as easy to walk a certain distance around a sphere as it would be to walk the same distance in a straight line?

 

[Jeff7]

Up and down would depend upon how you define your coordinate system.

 

[DrPizza]

Problem 2: both cars sweep out an equal volume, therefore each will be hit by the same number of raindrops. However, this ignores aerodynamic effects.

 

[sao123]

Originally posted by: Jephph

Originally posted by: Atomic Playboy
#1 Up and down are just our perceptions based on gravity. If we assume the sphere is the source of the gravity, then we will not feel we are moving up or down, but simply forward (similar to walking across the giant sphere we currently live on). If the sphere is not the source of gravity, then any perception of up or down will come from whatever the source of gravity is. If you were in a weightless environment, and the sphere were small enough that its gravitational effect on you were imperceptable, you would not feel as though you were moving up or down; it'd be more of a floating sensation.

Fun fun. So if we get rid of the gravity aspect, it would be just as easy to walk a certain distance around a sphere as it would be to walk the same distance in a straight line?

negative... if the source of gravity were non existent, or outside the surface of the sphere, walking around its entire surface would be virtually impossible.


as for question 2, if one can assume a uniform density of rainfall in drops per area then the answer is they get hit by the same number of rain drops. if the density is nonuniform, then you will be delving deep into calculus for the answer.

 

[Suspicious-Teach8788]

Originally posted by: CraKaJaX

Originally posted by: Jephph


#2, speed doesn't have anything to do with it. I would say it would be the size of the windshield and how fast the rain is coming down...

Hence the disclaimer of identical cars and the rain coming down at the same rate, same pattern, etc.

Rate at which raindrops hit the windshield is speed dependent.

Imagine your hand passing through the rain. Liek imagine bitchslapping a raindrop. Do it at a million miles an hour. In 1 second you can slap let's say 200,000 raindrops. If you do this at 0.0001 mph, you might hit 1 drop in 1 second.

Flux is dependent on relative speed, and so if your relative speed between the windshield and drops is different, you will have different # of drops hitting.

Now, a lot of people are reading "rain falls at the same rate." Ok, this isn't clear. If it's saying the rain falls at the same rate relative to passengers in both cars, then the answer is obvious. It's like saying person A observed 500 drops, and person B observed 500 drops. Duh it's the same, but I don't htink that's what the question is getting at. It's more like saying the rain is falling at the same rate in both environments, and so will varying the speed affect the # of drops/second hitting?

I say yes. But please someone point out the flaw in my thinking before I start viciously defending my view like some people do with teh airplane/treadmill problem.

Originally posted by: DrPizza
Problem 2: both cars sweep out an equal volume, therefore each will be hit by the same number of raindrops. However, this ignores aerodynamic effects.

But volume is not the question here. We're dealing with drops hitting in a time period, which involves flux. You're no longer dealing with constants but with rates and time dependent things. Just based on the fact that speed is a time dependent variable, it's enough to say that changing this time dependent variable will alter the rate at which drops hit the car windshields.

Edit. I misread the speed. I thought it was 60 and not 65 for Car B. From initial analysis it may seem that the drops are teh same, but if integration is required to calculate this, we might be dealing with something different.