Solve the following problem using analytical techniques: Suppose you walk 17.5 m straight west and then 24.0 m straight north. How far r you from your starting point, & what is the compass direction of a line connecting your starting point to your final?

Question

(If you represent the two legs of the walk as vector displacements A and B, as in the figure below, then this problem asks you to find their sum
R = A + B. Give the direction in degrees north of west.)

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Answer 1 · 2017-07-18T11:34:04

Simply calculate your hypotenuse and angle

You first went to West and North.

Your hypotenuse is your total distance from the starting point:

#R^2 = A^2 + B^2#

#R^2 = 17.5^2 + 24^2#

#R^2 = 306.25 + 576#

#R=sqrt(882.25) = 29.7# meters

However it is not a right statement that #R=A + B# (The statement provided on the figüre is WRONG!).

Your direction is northwest.

Now use trigonometry:

#sintheta= B/R#

#sintheta= 24/29.70 = 0.808#

#theta = 53.9# degrees. This is your angle.