## Poll

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2 votes (25%) | |||

2 votes (25%) | |||

1 vote (12.5%) | |||

1 vote (12.5%) | |||

1 vote (12.5%) | |||

1 vote (12.5%) |

**8 members have voted**

May 10th, 2019 at 4:56:56 PM
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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.

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.

May 10th, 2019 at 5:07:55 PM
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Round or square wheels?

Have you tried 22 tonight? I said 22.

May 10th, 2019 at 5:11:16 PM
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Quote:GialmereRound or square wheels?

Good one!

It's not whether you win or lose; it's whether or not you had a good bet.

May 10th, 2019 at 6:43:59 PM
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But can you pop a wheelie?

May 10th, 2019 at 10:55:51 PM
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Quote:SkittleCar1But 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.

May 11th, 2019 at 8:41:19 AM
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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.

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

May 11th, 2019 at 10:38:29 AM
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How do you know all this?Quote:WizardNathan 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.

May 11th, 2019 at 11:42:21 AM
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Quote:MichaelBluejayHow 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.

May 11th, 2019 at 12:07:18 PM
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Quote:WizardThe 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

May 11th, 2019 at 8:31:47 PM
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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 Tn

^{2}/ 2

An = 1 / (Tn - 2)

40 = Tn

^{2}/ (Tn - 2)

Tn = 20 + sqrt(320)

15 = Am (Tm - 5)

^{2}/ 2

20 = Am Tm

^{2}/ 2

Am = 1 / (Tm - 5/2)

40 = Tm

^{2}/ (Tm - 5/2)

Tm = 20 + sqrt(300)

Miplet wins