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 68
?
with the
positive x axis. The resultant displacement
has a magnitude of 8.6 m directed at an angle
of 108
?
from the positive x axis

Find the magnitude of the second displacement.
Answer in units of m


Find the angle of the second displacement
(measured from the positive x axis, with counterclockwise positive and within the limits of
-180? to +180?).
Answer in units of '

Explanation / Answer

First displacment s = 11 cos 68 i + 11 sin 68 j                               = 4.12 i + 10.199 j Resultant displacment S = 8.6 cos 108 i + 8.6 sin 108 j                                      = -2.657 i + 8.179 j Second displacment s ' = ? We know S = s + s'                 s ' = S - s                     = -2.657 i + 8.179 j -4.12 i - 10.199 j                     = - 6.777 i -2.0199 j The magnitude of the second displacement s ' = [ (-6.777) 2 + (-2.0199) 2 ]                                                                      = 7.071 m Let the second displacement vector makes an angle with negative x axis along negative y axis then       tan = 2.0199 / 6.777             = 16.59 o
Angle with positive x axis = 180 +                                         = 196.59 o

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