Mocha
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Post by Mocha on Feb 19, 2018 14:04:05 GMT
This puzzle is modified from one I read a few weeks ago. Hopefully it will make you think, and not just about math!
A two cars are driving down a straight road, parallel, in the same direction. The cars are identical.
One car is travelling at 70 mi/h, the other is travelling 80 mi/h.
Once the faster car overtakes the smaller car, they both simultaneously notice a fallen tree blocking the road.
(ie. they are both the same distance from the tree)
They both immediately begin to brake.
The slower car barely stopped a hair's width away from the tree.
However, logically, that means the faster car hit the tree.
How fast did the faster car hit the tree?
Bonus Question 1:
At what speed would the fast car have to be travelling for the impact speed to be 20 mi/h?
Bonus Question 2:
The same scenario as the original, but instead of 70 mi/h, x mi/h, and instead of 80 mi/h, (x+10) mi/h.
All three problems are solveable, either with calculus alone, or with algebra + physics. There is no tricky wording, but if you don't think carefully, you'll derive the trick answer instead of the correct one. As a super bonus for those who can solve it both ways, prove the formula you learned in physics to be true using calculus!
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Post by Polaris on Feb 19, 2018 16:42:23 GMT
i have no idea!!!!
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Mocha
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A Puzzle
Feb 19, 2018 16:45:37 GMT
via mobile
Post by Mocha on Feb 19, 2018 16:45:37 GMT
As a hint for the algebra + physics solution: use the kinematic equations |
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Post by fschmidt on Feb 19, 2018 19:57:29 GMT
This can't be answered without physics. I don't know how resistance (braking) works. I need to know the change in speed as a function of the speed.
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Mocha
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Post by Mocha on Feb 19, 2018 20:38:24 GMT
This can't be answered without physics. I don't know how resistance (braking) works. I need to know the change in speed as a function of the speed. >This can't be answered without physics. It can. >I don't know how resistance (braking) works. Braking is acceleration. >I need to know the change in speed as a function of the speed. You do not need to find the acceleration to solve the problem. |
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Post by Polaris on Feb 19, 2018 22:39:21 GMT
This is beyond me
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Post by Elizabeth on Feb 19, 2018 23:12:24 GMT
How can the faster car overcome the slower car and still be the same distance from the tree? This problem is confusing.
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Mocha
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Post by Mocha on Feb 19, 2018 23:13:51 GMT
How can the faster car overcome the slower car and still be the same distance from the tree? This problem is confusing. At the instant the faster car overtakes the slower car (ie. they are the same distance from the tree), they both brake. |
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Post by Elizabeth on Feb 19, 2018 23:17:53 GMT
How can the faster car overcome the slower car and still be the same distance from the tree? This problem is confusing. At the instant the faster car overtakes the slower car (ie. they are the same distance from the tree), they both brake. So they both were at the same place and going same distance when they saw it and braked? Then both missed hitting it or the other didn't break as hard and just barely hit it it would mean. |
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Mocha
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Post by Mocha on Feb 19, 2018 23:23:23 GMT
At the instant the faster car overtakes the slower car (ie. they are the same distance from the tree), they both brake. So they both were at the same place and going same distance when they saw it and braked? Then both missed hitting it or the other didn't break as hard and just barely hit it it would mean. >So they both were at the same place and going same distance when they saw it and braked? They weren't in the same place but they were the same distance. >Then both missed hitting it Not quite  > or the other didn't break as hard It is assumed they both brake at exactly the same rate >and just barely hit it it would mean. I wouldn't quite describe it as 'barely', but yes. :^) |
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Post by Elizabeth on Feb 19, 2018 23:29:57 GMT
That's why I asked my first question because story seemed to contradict. Then you said they're same distance from the tree so means they caught up to each other so would break around same time but one couldn't taken longer to break because of the shock or something. So I can't solve without a picture then I guess.  |
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Mocha
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Post by Mocha on Feb 19, 2018 23:34:56 GMT
That's why I asked my first question because story seemed to contradict. Then you said they're same distance from the tree so means they caught up to each other so would break around same time but one couldn't taken longer to break because of the shock or something. So I can't solve without a picture then I guess.  Ask and ye shall receive |
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Deleted
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Post by Deleted on Feb 24, 2018 21:33:17 GMT
I don't know how to use here calculus. I'll try to just using simple thoughts about it.
Identical cars = m1=m2; the brake system works equally.
distance to the tree = s1=s2;
spending time to the point = t1=t2;
Force of the faster car = m1a1.
Accelatarion = -v1t1^2;
Firstly, it blimps to eyes, if the almost all parameters of cars are the same, then is it true that the only the difference between is speed?
Secondly, should we pay attention to the force of cars before they noticed the tree?
The question was - how fast. So, I don't know, I think it's fully based on the speed, but I don't really know how.
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Post by Elizabeth on Feb 25, 2018 4:41:17 GMT
It's pure physics. I don't like physics.
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Post by Deleted on Mar 1, 2018 12:18:20 GMT
No, I've mistaken; surely t1 not equals t2, or else answer will have been answered already. Hard case for me. Long time no practice in physics. ElizabethIt's not fully physics, Mocha said that this riddle can be solved without any physics. I'd say we need more concentration and imagination to solve it. But, also he said that the puzzle use calculus... Coordinate system, perhaps would come in handy there. |
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