You know you love math
02-18-2011 | 11:11 PM
#1
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From: Williamsburg, VA
You know you love math
Car A is traveling at a constant speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
02-18-2011 | 11:22 PM
#5
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From: Williamsburg, VA
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02-19-2011 | 01:11 AM
#9
this question doesnt have anything to do with physics hahaha unless you bring masses and forces into it (acceleration is already present but no parameters are given to solve the acceleration)......F=ma
there are an infinite number of solutions because you have not given enough initial conditions to solve the problem
a singularity function might be necessary to solve this without more info
unless i am really drunk (which i am a little) and am missing something lol
30(a) + 3.5x - x(y) = y
yeah im too drunk to think about this lol
there are an infinite number of solutions because you have not given enough initial conditions to solve the problem
a singularity function might be necessary to solve this without more info
unless i am really drunk (which i am a little) and am missing something lol
30(a) + 3.5x - x(y) = y
yeah im too drunk to think about this lol
02-19-2011 | 07:15 AM
#10
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From: NYC
Car A is traveling at a constant speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
02-19-2011 | 07:56 AM
#11
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From: Charleston, SC
There are way too many unknowns in your original problem. For example, the rate of acceleration of car B before getting up to speed, which would help determine where it was at after 30 seconds (we know that car A was 0.67 miles further down the road after 30 seconds).
But, my assumption is that A is traveling at 80 mph, which means it's covering 1.33 miles per minute. So it takes it 2.625 minutes to travel 3.5 miles. So assuming car B doesn't start the pursuit until 30 seconds after car A passes, then it would have to cover 4.167 miles in 2.625 minutes (since car A would have traveled 0.67 miles in 30 seconds). This ends up being roughly 95.25 mph.
If car B waiting only 20 seconds, it would only have to travel at 90.16 mph to catch up.
Of course, I'm making assumptions that don't fall in line with your original question (like instantaneous acceleration), but then again, the original questions doesn't make *perfect* sense, because why would car B be pursuing car A at a constant speed? Most "car Bs" continue accelerating until they catch "car A" or until their speed is considered unsafe (which is likely higher than 95mph).
But, my assumption is that A is traveling at 80 mph, which means it's covering 1.33 miles per minute. So it takes it 2.625 minutes to travel 3.5 miles. So assuming car B doesn't start the pursuit until 30 seconds after car A passes, then it would have to cover 4.167 miles in 2.625 minutes (since car A would have traveled 0.67 miles in 30 seconds). This ends up being roughly 95.25 mph.
If car B waiting only 20 seconds, it would only have to travel at 90.16 mph to catch up.
Of course, I'm making assumptions that don't fall in line with your original question (like instantaneous acceleration), but then again, the original questions doesn't make *perfect* sense, because why would car B be pursuing car A at a constant speed? Most "car Bs" continue accelerating until they catch "car A" or until their speed is considered unsafe (which is likely higher than 95mph).
02-19-2011 | 08:02 AM
#12
Car A is traveling at a constant speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
Assume it takes Car B 30 seconds to get up to speed (since it was, you know, very well hidden off the side of a road between bushes)
Car B catches up with Car A in 3.5 miles after Car B reaches it's final and constant speed.
Identify the potential speed Car B was travelling at, base on practical assumpsions for Car A on a two-lane highway.
---
Now repeat excercise, and assume Car B took only 20 seconds to get up to speed.
02-19-2011 | 08:05 AM
#13
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From: Williamsburg, VA
Just because you don't want to follow the original assumptions, doesn't mean it can't be done [credit where credit is due, I believe my wife wrote that on one of her student's papers the last time one of the snowflakes thought they were too special to follow directions]. Not every problem has a closed form solution.
The asumptions given simplify what you'd need to do to provided bounds to the answer for this problem.
Multivariable Optimization is your friend, when it comes to engineering....
And when you need to quickly provide an estimate to a problem with multiple unknowns.
Try going 95 mph on a two lane road . . .
The asumptions given simplify what you'd need to do to provided bounds to the answer for this problem.
Multivariable Optimization is your friend, when it comes to engineering....
And when you need to quickly provide an estimate to a problem with multiple unknowns.
There are way too many unknowns in your original problem. For example, the rate of acceleration of car B before getting up to speed, which would help determine where it was at after 30 seconds (we know that car A was 0.67 miles further down the road after 30 seconds).
But, my assumption is that A is traveling at 80 mph, which means it's covering 1.33 miles per minute. So it takes it 2.625 minutes to travel 3.5 miles. So assuming car B doesn't start the pursuit until 30 seconds after car A passes, then it would have to cover 4.167 miles in 2.625 minutes (since car A would have traveled 0.67 miles in 30 seconds). This ends up being roughly 95.25 mph.
If car B waiting only 20 seconds, it would only have to travel at 90.16 mph to catch up.
Of course, I'm making assumptions that don't fall in line with your original question (like instantaneous acceleration), but then again, the original questions doesn't make *perfect* sense, because why would car B be pursuing car A at a constant speed? Most "car Bs" continue accelerating until they catch "car A" or until their speed is considered unsafe (which is likely higher than 95mph).
But, my assumption is that A is traveling at 80 mph, which means it's covering 1.33 miles per minute. So it takes it 2.625 minutes to travel 3.5 miles. So assuming car B doesn't start the pursuit until 30 seconds after car A passes, then it would have to cover 4.167 miles in 2.625 minutes (since car A would have traveled 0.67 miles in 30 seconds). This ends up being roughly 95.25 mph.
If car B waiting only 20 seconds, it would only have to travel at 90.16 mph to catch up.
Of course, I'm making assumptions that don't fall in line with your original question (like instantaneous acceleration), but then again, the original questions doesn't make *perfect* sense, because why would car B be pursuing car A at a constant speed? Most "car Bs" continue accelerating until they catch "car A" or until their speed is considered unsafe (which is likely higher than 95mph).
02-19-2011 | 08:06 AM
#14
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From: Williamsburg, VA
