physics-what am i doing wrong?

Question

a car travels three quarters of a lap on a circular track of radius R...
describe the magnitude of the displacement:
d=3(2piR)/4
i know the answer is greater than R but less than 2R, but i don't understand why?
can you also explain algebraically why when R=50m, the displacement is 71m...when i plug 50 in, i get 235m...i think i have lost it!!!!

SteveA8 · Accepted Answer

I think our problem is you are missing the question.  It is not how far has the car travelled, it is how mh distance is there from where it started, to where you are taking your measurement.  To do that, you have to measure the length of the chord from where it begn, to where 3/4 of the track is circled.

Think of it this way, if he completes the lap, the total displacement is zero

Anonymous · Answer

The displacement is a vector pointing from the beginning position to the final position.
So, let's assume your coordinate system is the xy graph from Cartesian geometry.
Then, your starting position  is point (50,0) and the ending position is (0,-50).
Draw a triangle (right triangle) with both sides equal to 50. Then the hypotenuse is 
h = (50 * 50 + 50 * 50 ) ^ 0.5
   = 71
hth.

Anonymous · Answer

you have the wrong equation.

physics-what am i doing wrong?

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