Fernanda is working on a physics project. she is experimenting by rolling a marble down a ramp and then seeing how far it rolls
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Answer:
162 km
Explanation:
A diagram can be helpful.
Using the law of cosines, we can find the magnitude of the distance (c) to satisfy ...
c^2 = a^2 +b^2 -2ab·cos(C)
where C is the internal angle of the triangle of vectors and resultant. Its value is ...
180° -39.8° -59.9° = 80.3°
Filling in a=76 and b=156, we get ...
c^2 = 76^2 +156^2 -2·76·156·cos(80.3°) ≈ 26116.78
c ≈ √26116.78 ≈ 161.607
The magnitude of the total displacement is about 162 km.
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Please note that in the attached diagram North is to the right and East is up. That alteration of directions does not change the angles or the magnitude of the result.
