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Wizard
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Wizard
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Thanks for this post from:
MrCasinoGames
May 10th, 2019 at 4:56:56 PM permalink
Nathan and Miplet have a unicycle race. Each has a uniform acceleration from a standing start.

Nathan covers the last 1/5 of the distance in 4 minutes. Miplet covers the last 1/4 of the distance in 5 minutes. Who won?

For the beer, I'd like to not just see a common sense answer but something showing the acceleration of both, for which you may assume a total distance of 1.

24-hour hold rule applies.
It's not whether you win or lose; it's whether or not you had a good bet.
Gialmere
Gialmere
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Thanks for this post from:
MrCasinoGames
May 10th, 2019 at 5:07:55 PM permalink
Round or square wheels?
Have you tried 22 tonight? I said 22.
Wizard
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Wizard
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May 10th, 2019 at 5:11:16 PM permalink
Quote: Gialmere

Round or square wheels?



Good one!
It's not whether you win or lose; it's whether or not you had a good bet.
SkittleCar1
SkittleCar1
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May 10th, 2019 at 6:43:59 PM permalink
But can you pop a wheelie?
Wizard
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Wizard
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May 10th, 2019 at 10:55:51 PM permalink
Quote: SkittleCar1

But can you pop a wheelie?



Not on a unicycle, without breaking the law of gravity.
It's not whether you win or lose; it's whether or not you had a good bet.
DogHand
DogHand
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May 11th, 2019 at 8:41:19 AM permalink
Wizard,
Here is my answer.



For constant acceleration a, if the initial velocity is 0, the distance traveled x is
x = a*t²
The time to reach a given distance x is given by t = √(x/a).
In the race, both N and M cover the same distance d (assumed to be 1 mile), so whoever requires less time is the winner.
Each contestant covers the final fraction f of the total distance in a time of ∆t.
Thus, ∆t = (time to reach d) - (time to reach (1-f)*d)
∆t = √(d/a) - √(d*(1-f)/a))
∆t = √(d/a)*(1 - √(1-f))
Solving for the constant acceleration a gives
a = d*(1 - √(1-f))²/(∆t)²
N covers the last f_N = 1/5 of the distance in ∆t_N = 4 minutes, so
a_N = (1 mile)*(1 - √(1-0.2))²/(4 min)² = 0.0006966... miles/min²
M covers the last f_M = 1/4 of the distance in ∆t_M = 5 minutes, so
a_M = (1 mile)*(1 - √(1-0.25))²/(5 min)² = 0.0007179... miles/min²
The time each requires to finish the distance d is
t_N = √(d/a_N) = √((1 mile)/(0.0006966... miles/min²)) = 37.88... min
t_M = √(d/a_M) = √((1 mile)/(0.0007179... miles/min²)) = 37.32... min
Therefore, M wins by just over a half minute.



Dog Hand

Edit: fixed a typo in spoiler.
Last edited by: DogHand on May 11, 2019
MichaelBluejay
MichaelBluejay
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May 11th, 2019 at 10:38:29 AM permalink
Quote: Wizard

Nathan and Miplet have a unicycle race. Each has a uniform acceleration from a standing start. Nathan covers the last 1/5 of the distance in 4 minutes. Miplet covers the last 1/4 of the distance in 5 minutes.

How do you know all this?
Wizard
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Wizard
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May 11th, 2019 at 11:42:21 AM permalink
Quote: MichaelBluejay

How do you know all this?



The Great and Powerful Wizard knows all!
It's not whether you win or lose; it's whether or not you had a good bet.
Nathan
Nathan
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May 11th, 2019 at 12:07:18 PM permalink
Quote: Wizard

The Great and Powerful Wizard knows all!



Hey, a Wizard Of Oz reference! 😁
In both The Hunger Games and in gambling, may the odds be ever in your favor. :D "Man Babes" #AxelFabulous "Olive oil is processed but it only has one ingredient, olive oil."-Even Bob, March 27/28th. :D The 2 year war is over! Woo-hoo! :D I sometimes speak in metaphors. ;) Remember this. ;) Crack the code. :D 8.9.13.25.14.1.13.5.9.19.14.1.20.8.1.14! :D "For about the 4096th time, let me offer a radical idea to those of you who don't like Nathan -- block her and don't visit Nathan's Corner. What is so complicated about it?" Wizard, August 21st. :D
ThatDonGuy
ThatDonGuy
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May 11th, 2019 at 8:31:47 PM permalink

This is easier to solve if the distance is 20

From a standing start with constant acceleration, distance =acceleration x time squared

Let An and Am be Nathan and Miller's accelerations, and Tn and Tm their total times in minutes.

16 = An (Tn - 4)2 / 2
20 = An Tn2 / 2
An = 1 / (Tn - 2)
40 = Tn2 / (Tn - 2)
Tn = 20 + sqrt(320)

15 = Am (Tm - 5)2 / 2
20 = Am Tm2 / 2
Am = 1 / (Tm - 5/2)
40 = Tm2 / (Tm - 5/2)
Tm = 20 + sqrt(300)

Miplet wins


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