A particle undergoes two displacements, measured from the positive x-axis, with

Question

A particle undergoes two displacements, measured from the positive x-axis, with counterclockwise positive. The ?rst has a magnitude of 11 m and makes an angle of 66 ? with the positive x axis. The resultant displacement has a magnitude of 9.8 m directed at an angle of 124 ? from the positive x axis. Find the magnitude of the second displacement. Answer in units of m
013 (part 2 of 2) 10.0 points Find the angle of the second displacement (measured from the positive x axis, with counterclockwise positive and within the limits of -180 degrees to 180 degrees) Answer in degree

Explanation / Answer

First displacment s = 11 cos 66 i + 11 sin 66 j                               = 4.474 i + 10.04 j Resultant displacment S = 9.8 cos 124 i + 9.8 sin 124 j                                       = -5.48 i + 8.124 j We know S = s + s ' From this second displacment s ' = S - s                                                    = -5.48 i + 8.124 j - 4.474 i - 10.04 j                                                    = -9.954 i -1.915 j Magnitude of second displacment s ' = [(-9.954) 2 +(-1.915) 2 ]                                                          = 10.13 m Let s ' makes an angle with negative x axis then tan = 1.915 / 9.954                                                                                  = 10.88 o Angle with positive x axis = 180 +                                         = 190.88 o

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