The Chicken From Minsk Thread

[Aircraft Aviation 2]

These particular questions are not representative of the difficulty seen later in the book. In fact, this title is entitled "warm up questions".

[J G 927]

Bring it on! I say.

[Aircraft Aviation 2]

Problem #19

 

Adventures on the Moscow Subway - Boris commutes to college by the Moscow subway, which runs in a circle. The school happens to be at the point on the circle that is exactly opposite to where Boris boards the train, so it takes the same time to get to school by train in either direction, and trains run in both clockwise and counterclockwise directions. The train schedules are very regular. The time interval between two successive counterclockwise trains is the same as for trains moving in the other direction; for instance, if there is an hour between the arrival of clockwise trains, there is also and hour between the arrival of counterclockwise trains. Boris observed, however, that he caught the clockwise trains more often than the counterclockwise ones, despite the fact that his schedule was irregular and he arrived at the station at random times. Can you explain this?

[J G 927]

From the narrative we understand that:

Clockwise trains run at the same interval as anti-clockwise trains.

The distance from journey start to journeys end is the same.

The train journeys both take the same time, so the train speeds must be the same.

 

What we are not told is the arrival times of the trains at the journey's start, and this is what is key to the frequency of the direction of the train caught.

 

Lets say that the trains are every half hour. If the trains clockwise train arrived at the top of the hour and the half hour and the anticlockwise train at quarter to the hour and quarter past the hour, there would be an even 15 min. interval between trains.  If you arrived at the station at a random time you would have an even chance of catching a train in either direction.

 

This is not happening.  We can therefore deduce that the interval between the clockwise train and the anti-clockwise train is less than the following interval between the anti-clockwise train and the next clockwise train.

 

Lets say the clockwise train arrives on the hour and half hour and the anti-clockwise train arrives at 5 past the hour and 35 past the hour. If you randomize arrival time of Boris to catch a train, he will have more chance in arriving in the longer gap and therefore of catching the the clockwise train.

 

 

[allardjd 1,853]

Yup.

 

John

[Andrew Godden 945]

This new learning amazes me, Sir Bedevere.  Explain again how sheeps' bladders may be employed to prevent earthquakes. 

 

Cheers

Andrew

[J G 927]

Something to do with Birds droppings frightening the earth as I recall. 

 

Fish bladders can help here as well.

 

Finings used to clear newly brewed beer are made from fish bladders (I don't want to put you off beer guys).

 

They are added as a last process and cause the suspended particles to drop the the bottom of the barrel as sediment.

 

This allows you to drink copious amounts of beer and then you so pi**ed you don't notice the earth moving.

 

Who on earth once thought " Hmm this beer is cloudy.... I know! I add those fish bladders from last nights supper to the beer and see what happens!)

 

 

[Aircraft Aviation 2]

Correct.

[Aircraft Aviation 2]

Problem #20

 

The Crazy Dog - Misha and Tisha are on their bicycles, a distance L apart. They begin at the same time to move toward each other, each pedaling as fast as he can, intending to collide. At the instant they begin, their dog, who loves them both, leaves Misha and runs as fast as he can to Tisha, who pats him on the head. When this happens, he leaves Tisha and runs back to Misha, who also pats him on the head, at which point he turns and runs back to Tisha. All this is repeated until the bicyclists collide. How much distance is covered by this crazy, affectionate animal? Assume that Misha and Tisha move with constant speeds v1 and v2, respectively, and the dog moves with speed u and is able to turn around instantaneously (he tries!).

 

No excuse for getting this one wrong .

[J G 927]

U-(V+V1)

-----------

      L

 

 

Edit:- Hmmm I'm not sure this is correct

[Aircraft Aviation 2]

Indeed John, it isn't correct! About time we had a break in the chain of right answers .

 

NOTE: I have changed "v" in the original post to "v2" (as it should be). This still, however, won't change your answer (feel free to leave v2 as v if you want).

[Kasper 14]

Annoying as it is that the questions are not correct (in the sense that I should at least know the Units of L and V)

The answer is:

(L/(V1+V2))*U

Assuming that it is not km/hr and Miles or Knots or ....

[Aircraft Aviation 2]

Hi Kasper,

 

It shouldn't matter what the units are; we're doing this all algebraically - the question is perfectly correct. All you need to know is that L is a length and that V and U are velocities; you aren't trying to get any sort of numerical answer. In fact, even if v1 and v2 were in "different" units, it wouldn't matter; since they could be converted directly between one another. A problem would arise if v1 and v2 were the wrong types of unit; perhaps if one was a velocity, and the other a volume; then you wouldn't be able to solve it. This particular realm is called dimensional analysis, and I've been doing a fair bit of it recently (most notably in the Physics Olympiad papers). 

 

And yes, your answer is entirely correct.

[brett 2,316]

You guys should work on 'The Hodge conjecture' and split the million.

[jaydor 345]

Problem #20 = Misha &Tisha would be better off on a bicycle made for 2..

[Kasper 14]

I don't totally agree because L/(V1+V2) is Time. So L and V should be km km/hr  nm / knots etc. L = km and V = knots would need another mathematical operation to make the outcom Time * U correct.

[Aircraft Aviation 2]

But Km/Nm/Furlongs/mm/m/lightyears are all units of distance. Provided that they are lengths, it doesn't matter; it would matter if they were different types of unit (eg one a velocity, the other a volume or a temperature) - that wouldn't work. Consider the following (and bonus points to whoever gets this):

 

 

 

Note that not a single number or unit is given.

[Aircraft Aviation 2]

I'll award one point to anyone who can get at least 3 marks on the above question, two to anyone who can get at least 5, and four to anyone who gets full marks. Your answers will be marked by yours truly, since of course, Oxford do not release mark schemes for their Physics papers .

[J G 927]

For Part (a)

 

Kinetic Energy of car = Power * time.

 

E = P * T

 

Velocity = Sq root of ((2*E)/M)  where M is the mass of the car. (derived from E=1/2 MV²)

 

 

 

I think......  I could be wrong though.  I will rest my brain until that is marked and then maybe go on to part (b) later. 

[Aircraft Aviation 2]

Hi John,

 

E is definitely equal to P*t

 

The second part of your answer, whilst correct, doesn't quite answer the question. The questions asks for velocity as a function of time. Don't worry though, only a very minor correct is required .

[J G 927]

T=E/P

[Aircraft Aviation 2]

Nope... The second part of your answer needs changing, not the first! E = P*t is correct.