Two Beetles Two beetles run across flat sand,starting at the same point. Beetle

Question

Two Beetles Two beetles run across flat sand,starting at the same point. Beetle 1 runs 0.50 m due east, then0.86 m at 28° north of due east. Beetle 2 also makes tworuns; the first is 1.6 m at 47°east of due north. (a) What must be the magnitude of its secondrun if it is to end up at the new location of bettle one?
?m
(b) What must be the direction?
?° (counterclockwise from due east) (a) What must be the magnitude of its secondrun if it is to end up at the new location of bettle one?
?m
(b) What must be the direction?
?° (counterclockwise from due east)

Explanation / Answer

let the unit vector in east direction be i and north be j thenthe displacements of 1 st runner S = 0.5 i + 0.86 cos 28 i + 0.86 sin 28 j = 0.5 i + 0.7593 i + 0.4037 j = 1.2593 i +0.4037 j displacement of 2 nd runner S ' = 1.6 sin 47 i + 1.6 cos47 j                                                = 1.17 i + 1.091 j So, displacement of 2 nd runner to end up is S " =S - S '                                                                           = 0.0893 i -0.6874 j Magnitude of S " = [ 0.0893^2 + (-0.6874 ) ^ 2]                           = 0.6931 m Let the S" makes an angle with east directionthen tan = -0.6874 / 0.0893                                                                                      = -82.59 degrees In counterclockwise direction ' = 360 -                                                    = 277.4degrees                                                                                       

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