While playing a scavenger hunt game, Anthony walks 48.0 m to the south and then walks 12.0 m to the west. What single straight-line displacement could Anthony have taken to reach this point?

Question

23-06-2016
Physics

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While playing a scavenger hunt game, Anthony walks 48.0 m to the south and then walks 12.0 m to the west. What single straight-line displacement could Anthony have taken to reach this point?

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metchelle metchelle · Answer 1 · 2016-06-30T06:19:19+02:00

As these are distances created by moving in a straight line, using a trigonometric analysis can solve the missing single straight-line displacement. Looking at the 48m and 12m movements as legs of a triangle, obtaining the hypotenuse using the pythagorean theorem will yield us the correct answer.
This is shown below:

c^2 = 48^2 + 12^2
c = sqrt(2304 + 144)
c = sqrt(2448)
c = 49.48 m

To obtain the angle at which Anthony walks 49.48, we obtain the arc tangent of (12/48). This is shown below:

arc tan (12/48) =14.04 degrees.

Therefore, Anthony could have walked 49.48 m towards the S 14.04 W direction.