Posts by bb6

    I do have a question about # 13. I gat to 65 minutes minimum. The 5 minute walker takes the torch back 2x:

    25 + 5, 20 + 5, & 10 = 65 minutes. I don't see how it is possible to get them all across the bridge in 60 minutes?

    There is a quicker way though: let the 5 and 10 min walk first, then the 5min guy goes back (15 min passed), now the 20 and 25 min walk (40min passed) and the 10min guy goes back (50min passed), finally the 5 and 10min guy walk. So we get to the other side in 60min.

    There is hardly a way to tell what "the best" option is, since how good is "low" durability compared to "average" or "high". Furthermore how can I compare quality and price and punctuality? Isn't that comparing apples with pears?

    Moreover there could be many more criteria: consider that one company offers to deliver the components tomorrow, while another can only deliver then in a couple years time. In this case I wouldn't even consider the second company in my "purchasing plan for the upcoming year"...


    Anyway "A way" to decide comes down to the following:

    "Swiss" metal and "General Machines" have the same punctuality, so we can ignore that for now. "Swiss" is more expensive, but has greater quality than "General", since quality is more important than price, we choose "Swiss" over "General". The same holds when comparing "Swiss" with "Mega", on top of that "Swiss" has better punctuality than "Mega" thus we certainly choose "Swiss" over "Mega". Hence "Swiss metal" is the prefered company.

    First of all notice that (for an observer standing on a platform) the jupiter takes 620/300=2h 4min to reach Hicksburg.

    Option 1 would take a total time of 6h 4minto reach Hicksburg, thus the passengers will miss their connection in Hicksburg (we only have 5h 30min), thus the costs will add up to $38 000.

    Option 2 would cost a total of $16 000 (as half their ticket price is $8000), however now some passengers might be stuck in Stroudford...

    Option 3 would take 3h 34min to reach Hicksburg, thus passengers will be able to change at Hicksburg. The costs are now $12 000, plus some reimbursement for the delay.

    Option 4 would take us in 620/300/.4=5h 10min to Hicksburg, thus passengers will be in time to catch their connection. The cost will only be some reimbursement for the delay, but this will be less than $8000 , since the delay is smaller than in option 1.


    It should be clear that option 4 is preferred.

    Q1: B

    Q2: scissors

    Q3: A

    Q4: B

    Q5: A

    Q6: 10 rotations anti-clockwise

    Q7: 2.5kg

    Q8: 20cm (assuming pulleys are fixed)

    Q9: still A (assuming there is no friction)

    Q10: Less than 5 cm

    Addendum 2: looking carefully at the previous addendum, I created a paradox, suppose the observer would actually take (a very little more than) 30min to reach the switch. Then for the observer would see a collision, but the trains won't... absurd.

    The solution to this paradox is that I assumed that in the frame of each train, the observer starts running at the same time as the trains are 140/γ km apart. However simultaneity is not conserved between different frames, thus the observer would then start running and see the trains 140km apart at different times.

    Let us first look at the trains: using non-relativistic mechanics we see that from one train's perspective the other train is moving in with a speed of 160+120=280km/h. Hence the distance to the other train (140km) with be covered in exactly 30min. The supervisor needs to run 6.3km at a speed of 14km/h, thus takes 6.3/14=0.45h=27min. Since 27<30, the supervisor can pull the switch before he sees the trains collide.


    We only need to hope the switch is in the right place...


    Addendum: when considering the relativistic case, in the frame of the switch, the switch will be pulled in 27min (same calculation).

    In the frame of each train, the speed of the other train moving in, is slightly smaller than 280km/h (it is (120+160)/(1+120*160/c^2), where c^2 is the speed of light).

    In the frame of a train the distance to be covered will be shortened by a factor γ (which is different for both trains), so for the train the collision happens a factor γ earlier than for the switch. However the clock in each trains is running slower than the clock in the switch, by the same factor γ. So a train sees the switch being pulled earlier by a factor γ than the switch sees it.

    We conclude that both trains see the switch being pulled earlier than they "see" collision happen, in fact relativity will help avoid the collision.


    PS: γ=1/sqrt(1-v^2/c^2), where v is the speed of the train and c the speed of light