# Actual textbook physics problem

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When compared with physics, the science-ness of political â€śscienceâ€ť gets pretty low.

Letâ€™s use arbitrary units for distance, by multiplying km/h by minutes. (Weâ€™ll convert that later by a simple constant. This saves us a lot of multiplications and rounding errors.) Track the direction changes on a plane. Then count the distances in x and y, which is easy when operating in a carthesian grid; we increment or decrement just one, no need for sin/cos factors. (Okay, need, but they are always 1 or 0.) The rest is just a grind with paper and pen (better draw it to not get lost in all the direction changes).

steps (assume starting direction is north):
1: direction +00=N, 502=100
2: direction +90=E, 20
4=80
3: direction +90=S, 201=20
4: direction -90=E, 50
1=50
5: direction +90=S, 202=40
6: direction -90=E, 50
0.5=25
Adding up the directions, we get 100-20-40=40 N, and 80+50+25=155 E.
The total distance is sqrt(40^2+155^2)=160 units.
The direction related to the eastward direction is arcsin(40/160)=arcsin(0.25)=14.5Â° towards the north, or 75.5Â° clockwise from the initial direction.
As the units weâ€™re using are kilometers/hour*min, we have to multiply it by min/hour, or 1/60. So 160/60 is 2.67 km.

So we are 2.67 km away, 75.5 degrees clockwise from the direction we initially went.

The nest of the scourge known as political â€śscientistsâ€ť is within walking distance. Escape should not be that difficult.

â€¦I hope I did not make a stupid mistake in the calculationsâ€¦

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Jearl Walker, one of the authors, is a beloved physics professor at Cleveland State University. He just started posting YouTube videos from his class, The Flying Circus of Physics (the only Physics class I ever took that I passed.)

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If you can tell the speed of a vehicle from the whine of the engine youâ€™re clearly a superhero, and are unlikely to have any real problem dealing with this scenario.

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I disagree. I believe the answer is a 360 degree turn around, directly away from the goal, and we travel nowhere.

Hmmmmmâ€¦ Where did I make the mistake, then? My math got somewhat rusty and the WD40 only began to soak inâ€¦

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Drove through what soundedâ€¦

It sounded like a cocktail party.

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Iâ€™m fairly certain you are right and johnphantom is wrong. Before coming to the comments I scribbled it out with a post-it note and wolfram alpha (I didnâ€™t think of your km/h * minutes as a unit trick, so I had all the ugly rounding issues to deal with) and got the same answer as you for the distance. I didnâ€™t bother to calculate the exact angle, but itâ€™s definitely more North than South, so not due East. And you never travel West, so itâ€™s not due North either.

You made a mistake in understanding the density of the WD40.

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Kudos for the reference, but thatâ€™s the wrong field. The math symposium is down the hall. Just look for the conspiracy theorist guiding the blind hacker.

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Clearly you did not learn your lesson, so you are kidnapped again by political science majorsâ€¦

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Hilarious!

Grant denied.

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Is no one else upset at this being described as a physics problem? Seems like nothing more than a little trigonometry and vector additionâ€¦

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I got the same answer you did in a completely more labor intensive way than your rather elegant answer.

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A lot of physics is math in disguise. The field assignment fits.

â€¦and use the same method to escape, because they never learn from their mistakes.

I got to the middle of step 3 and only then I realized I have nice round easy to work with numbers and am spoiling them with an ugly constant that is the same for all the steps anyway.

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Related: Whenever my calculus teacher wants you to explain something in an intuitive/wordy way rather than using actual math, he says â€śExplain it like you would to the people downstairs.â€ť; downstairs hosting the communications department (marketing, etc.)

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I did it converting km/h into km/min and used rough vector addition and got 2,65 km.

Iâ€™m actually taking physics this semester (itâ€™s one of the options for CS Majors here in the University of Wisconsin system for fulfillment of breadth requirements.) As soon as I saw the text, I though it looked familiar. Iâ€™m using the 7th edition of this book and I can confirm that this problem appears in my book as well. I get along well with this professor (Iâ€™ve fixed his computer a time or two) and look forward to pointing it out at our next class.

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The divide-by-60 (or divide-by-3.6 if converting to m/s like I did at first) leads to some nasty periodic fractions and a corresponding additive rounding error.

Yes, thats why I wrote â€śroughâ€ť addition, I didnÂ´t take all the fractions down for the final addition