Puzzle for Halflife2.net

[xombine]

I think you fried all of our brains. :rolling:

That car thief one actually pisses me off its so confusing.

 

[Stigmata]

<bike problem>

All I know is that the bike is moving from left to right.

Only one of the following multiple choice answers is correct. Which is it?
A) Answer A
B) Answer A, and B
C) Answer B, and C

A. Answering with B or C means that either two or three of the answers is correct, and the question states only one is correct.

 

[ericms]

And here is one more even harder problem (even if not many people are trying these). Calculus might help but you can solve it without it:

On a certain winter day, snow starts to fall at a heavy and steady rate. Three identical snowplows start plowing the same road, the first leaving at 12 noon, the second leaving at 1 pm, and the third leaving at 2 pm. At some time later, they all collide. At what time did the snow start to fall?

Note: Assume that the speed of a snowplow is inversely proportional to the depth of the snow.

Would I get for a position value for a snowplow at time t, rate r of increasing snow depth, and constant c that which is below?

P(t) = ln(t)/r + c

So you're saying the snowplows all collide at once for some t? I'll have to think about this some more.

 

[Dan]

All I know is that the bike is moving from left to right.

A. Answering with B or C means that either two or three of the answers is correct, and the question states only one is correct.

Nope, if A were the answer, B says that A is correct, so B would be correct as well, making A incorrect.

All I know is that the bike is moving from left to right.

wrong

As for the snowplow problem. I think you need to refine your model more.

 

[Stigmata]

wrong

Touche.

 

[ericms]

As for the snowplow problem. I think you need to refine your model more.

I got it from saying dD/dt = r for some steady snow fall

D(t) = r*t + k

This is just r*t though (set t = 0) and if, as you said in your note, the speed of a snowplow is inversely proportional then

S(t) = 1/r*t or P(t) = ln(t)/r + c

 

[Dan]

There should be no constant c (snow below). Before the snowfall starts there is no snow on the ground, and after a snowplow has gone by, there will be no snow on the ground until it accumulates again. I also think that you might be interchanging the variable t. Otherwise I don't know what to make of your equations.

 

[ericms]

Right, I knew it would have to accumulate again or else the snowplows would never collide. I didn't set t=0 since P(t) isn't defined for it, but I guess it's implicit since it wouldn't have traveled anywhere.

BTW, did you get anywhere on the bicycle one?

 

[Dan]

BTW, did you get anywhere on the bicycle one?

If you must know, the bicycle goes right to left, B is the back wheel, A is the front. I don't really have much of a proof, I just pictured a bicycle moving along the tracks, and it's the only way that works. Well, I can prove that B is the back wheel because the tangent of A doesn't necessarily intersect B anywhere. And since the bicycle frame must be tangent to the back wheel and intersect the front wheel, B has to be the back.

As for your snowplow equations, you defined that t is time, but you seem to be using it as snow thickness as well which is confusing.

 

[Stigmata]

Well since the snowfall is a constant snowfall over time, instead of using two variables he can just use t with a coefficient to denote the amount of snow that falls per t.

 

[ericms]

Dan, I used time as a component of the depth of snow. You meant D(t), right?

 

[Dan]

Dan, I used time as a component of the depth of snow. You meant D(t), right?

Well make sure to keep your variables in order then and all referring to the same values. Because there are three difference depths and only one time. I think your equations underestimate the complexity of the problem. After taking a good look at the problem, if you solved it by brute force calculus you would need to know how to solve partial differential equations.