Actual textbook physics problem


#1

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#2

When compared with physics, the science-ness of political “science” gets pretty low.

Nice dead reckoning exercise/problem, too.

Let’s use arbitrary units for distance, by multiplying km/h by minutes. (We’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)=14.5° towards the north, or 75.5° clockwise from the initial direction.
As the units we’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 “scientists” is within walking distance. Escape should not be that difficult.

…I hope I did not make a stupid mistake in the calculations…


#3

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.)


#4

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


#5

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


#6

Hmmmmm… Where did I make the mistake, then? My math got somewhat rusty and the WD40 only began to soak in…


#7

Drove through what sounded…

It sounded like a cocktail party.


#8

I’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 didn’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 didn’t bother to calculate the exact angle, but it’s definitely more North than South, so not due East. And you never travel West, so it’s not due North either.


#9

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


#10

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


#11

Clearly you did not learn your lesson, so you are kidnapped again by political science majors…


#12

Hilarious!

Grant denied.


#13

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


#14

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


#15

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

…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.


#16

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


#17

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


#18

I’m actually taking physics this semester (it’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. I’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 (I’ve fixed his computer a time or two) and look forward to pointing it out at our next class.


#19

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.


#20

Yes, thats why I wrote “rough” addition, I didn´t take all the fractions down for the final addition :wink: