BR Physics Translat'l Motion, Ex. 1.3a

[MusicIsLife]

I'm sure this is super basic, but I'm not understanding BR's method of putting hash marks along a vector & the x- and y- axes. They seem to be using that to figure out the answers, but I can't follow their logic! I mean, where they use 3 hashes on the x-axis, I could easily use 5 or 6...I don't understand how you know how to divide up the axes like that...can someone help? I'm able to answer the questions through my own, long, drawn-out methods (w/ the complicated math) but that defeats the whole purpose of these neat tricks...if only I could follow!

Thanks

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[BerkReviewTeach]

I'm sure this is super basic, but I'm not understanding BR's method of putting hash marks along a vector & the x- and y- axes. They seem to be using that to figure out the answers, but I can't follow their logic! I mean, where they use 3 hashes on the x-axis, I could easily use 5 or 6...I don't understand how you know how to divide up the axes like that...can someone help? I'm able to answer the questions through my own, long, drawn-out methods (w/ the complicated math) but that defeats the whole purpose of these neat tricks...if only I could follow!

Thanks

It comes down to comparing the example to a 45-degree angle. If it covered 4km at a 45 degree angle, then the x (east) and y (north) components would be equal. Because it's more east than north, the x-vector (east) must be slightly greater than the y-vector (north). Pretty much only choice A meets that stipulation.

Now the reason these use hash marks of 2.something and 3.something has to do with the Pythagorean theorem.

• east^2 + north^2 = 4^2 = 16
  
  Assuming the numbers in choice A or C to be correct, let's plug in choice A.
  3.06^2 + 2.57^2 = 9.2 + 6.8 = 16.
  
  The attachment may explain it a bit better. It's from the new version of the physics book.