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 Posted: Tue Jan 08, 2008 1:04 pm
For some reason, this math problem was considered a joke too all of us (if not all at least most) when we were small and introduced to us.
If not, then the short summary:
On a straight frictionless track, two trains are facing each other x distance apart.
Train A weighting k1 starts and leaves at time t1 accelerating at a1 then remains a constant speed of v1.
Train B weighing k2 on the opposite side of the track leaves at time t2 accelerating at a2 then remains a constant speed of v2.
Assume no wind resistance. At what time will the two trains collide? What direction will the trains be going after the collision (assuming a 100% elastic and inelastic collision senarios)?
Thing is most of us encountered this "joke problem" with actual variable and assuming that x distance gives enough time for time t1 and t2 to make sense to be apart.
For the time of collision, the LONG way would be the simple track down a certain time interval and see how long the trains traveled...but as you can see that's just takes too freakin long stressed But out of curiousity I've attempted that but as it got down to milliseconds it just got more and more constraining.
Anyone remember the correct formula(s) to tackle this problem? I dunno, it's just been bugging me for awhile.
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Posted: Tue Jan 08, 2008 1:20 pm
I hate word problems. They can go die.
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Posted: Tue Jan 08, 2008 3:55 pm
Isn't it speed over time = rate? And then you can figure it out? I dunno. Bad at maths.
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Posted: Tue Jan 08, 2008 4:51 pm
[.SamusAran.] Isn't it speed over time = rate? And then you can figure it out? I dunno. Bad at maths. Speed over time (s/t) makes an average velocity, get it's derivative and you get instantanious velocity. But the problem is with that cooresponding value, trying to get when the two trains will "meet" is a dependant of that value. That is the formula that's needed.
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Posted: Tue Jan 08, 2008 6:25 pm
I'll try something.
I can tell that you'll have to compare both formulas at the end to know the time.
So since we're we know that x only get smaller, I suppose we'll have a divison or soustraction and that x will be in both forumulas (otherwise, we can't compare both of them).
Arg! I need numbers! gonk ARG! I CAN'T AWNSER! ARRGGG!!!!!
DARN IT ALL!!!
I am so mad that I'll study this question! scream
Must we find when the train stop accelerating?
ARG! SO MUCH VARIABLES WITHOUT NUMBERS! ARRRGGG!!!!
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Posted: Tue Jan 08, 2008 6:33 pm
Hrm....must find the common distance thus
train1=train2...so ARG! That comparaison should gives the distance of impact...AARRGG!
Replacing...that stuff...the distance obtened in one of the train formula should...give the time...
GGGGRRRRAAAAAA!!!! scream
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Posted: Tue Jan 08, 2008 6:53 pm
Prega Hrm....must find the common distance thus train1=train2...so ARG! That comparaison should gives the distance of impact...AARRGG! Replacing...that stuff...the distance obtened in one of the train formula should...give the time... GGGGRRRRAAAAAA!!!! scream Well if you want, you COULD assume the trains started at set velocity and ignore acceleratioin basically making each train already starting at that velocity. Also, to simply it even more, v1 = v2, t1 = t2, k1 = k2 I've tried that as well, but I've still gotten stuck >_>
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Posted: Tue Jan 08, 2008 8:02 pm
I've got a better one...
Snidely Whiplash has kidnapped the love of your life Nell and placed her on some train tracks shared by two trains facing each other approximately 20 miles apart.
Both trains start their engines at the same time, but Train A is moving 10 miles an hour faster than Train B. However Nell is 5 miles closer to Train B.
How long do you have to save your Love and defeat Snidely Whiplash?
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Posted: Tue Jan 08, 2008 8:14 pm
Let's ignore the acceleration because I've never seen it done that way and it just overcomplicates it.
Distance = velocity * time. You want to write the equation for each of the trains and see where the functions intersect.
d1=v1*T
d2=v2*T
You also know d1+d2=x, so d2=x-d1. Substitute that in:
d1=v1*T
x-d1=v2*T
Add the two equations together:
x=v1*T+v2*T
Rewrite:
T=x/(v1+v2)
You can also find d1 and d2, knowing T.
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Posted: Tue Jan 08, 2008 8:32 pm
AerisEsper Let's ignore the acceleration because I've never seen it done that way and it just overcomplicates it. Distance = velocity * time. You want to write the equation for each of the trains and see where the functions intersect. d1=v1*T d2=v2*T You also know d1+d2=x, so d2=x-d1. Substitute that in: d1=v1*T x-d1=v2*T Add the two equations together: x=v1*T+v2*T Rewrite: T=x/(v1+v2) You can also find d1 and d2, knowing T. Well thank you for that biggrin But I think I can factor acceleration into that equation, just give me a moment
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Bag of Monster Vice Captain
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Posted: Tue Jan 08, 2008 9:08 pm
3 velociraptors have you surrounded from all sides. They all have a max running speed of X with an acceleration of Y. The one to the north has an injured leg and his acceleration and max running speed are cut in half. Now, supposing they all attack simultaneously, how many shotgun bullets will it take to escape with minimal blood loss.
I wanna become a math teacher just to find a way to fit Dinosaurs into word problems.
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Posted: Tue Jan 08, 2008 9:09 pm
Part-Time Viking I've got a better one... Snidely Whiplash has kidnapped the love of your life Nell and placed her on some train tracks shared by two trains facing each other approximately 20 miles apart.
Both trains start their engines at the same time, but Train A is moving 10 miles an hour faster than Train B. However Nell is 5 miles closer to Train B.
How long do you have to save your Love and defeat Snidely Whiplash?5 miles close to Train B means that Nell is 15 miles from Train A and 5 miles from Train B. The easiest route would to say that the trains would arrive to crush Nell at the exact same time of 1 hour since 15 MPH is 10 over 5. However, we were never given what exactly what the trains' velocities are. So that's when we have to factor in equations. Let's see...double Train B's speed would be 10 MPH and would hit Nell in 30 minutes. So for Train A that would be 20 MPH and would hit Nell in 45 minutes. Double again Train B's speed and that's 20 MPH. So that's 15 minutes for smashing. That'd mean Train A is 30 MPH and that'd take 40 minutes. It seems like Train B's getting the advantage. Fastest train speed (bullet train) is 300 km/h and that translates to 186.411 MPH. Hold on, still figuring it out, just posting so my post doesn't go away
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Posted: Tue Jan 08, 2008 10:28 pm
Father Knows Best i Part-Time Viking I've got a better one... Snidely Whiplash has kidnapped the love of your life Nell and placed her on some train tracks shared by two trains facing each other approximately 20 miles apart.
Both trains start their engines at the same time, but Train A is moving 10 miles an hour faster than Train B. However Nell is 5 miles closer to Train B.
How long do you have to save your Love and defeat Snidely Whiplash?5 miles close to Train B means that Nell is 15 miles from Train A and 5 miles from Train B. The easiest route would to say that the trains would arrive to crush Nell at the exact same time of 1 hour since 15 MPH is 10 over 5. However, we were never given what exactly what the trains' velocities are. So that's when we have to factor in equations. Let's see...double Train B's speed would be 10 MPH and would hit Nell in 30 minutes. So for Train A that would be 20 MPH and would hit Nell in 45 minutes. Double again Train B's speed and that's 20 MPH. So that's 15 minutes for smashing. That'd mean Train A is 30 MPH and that'd take 40 minutes. It seems like Train B's getting the advantage. Fastest train speed (bullet train) is 300 km/h and that translates to 186.411 MPH. Hold on, still figuring it out, just posting so my post doesn't go away Okay, Train A uses Coal, whilst Train B uses diesel fuel... Have fun with that altercation wink
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Posted: Wed Jan 09, 2008 3:03 am
Also, Train B has a flux capacitor.
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Posted: Wed Jan 09, 2008 8:58 am
Remember how to do it? I never learned. <__<
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