A particle undergoes three displacements. The first has a magnitude of 15 m and

Question

A particle undergoes three displacements.
The first has a magnitude of 15 m and makes
an angle of 27 degrees with the positive x axis. The
second has a magnitude of 6.1 m and makes
an angle of 142 degrees with the positive x axis. (see
the figure below).
After the third displacement the particle

Find the angle of the third displacement (mea-
sured from the positive x axis, with counter-
clockwise positive within the limits of 180 degrees
to +180 degrees).
Answer in units of degrees.

A particle undergoes three displacements. The first has a magnitude of 15 m and makes an angle of 27 degrees with the positive x axis. The second has a magnitude of 6.1 m and makes an angle of 142 degrees with the positive x axis. (see the figure below). After the third displacement the particle Find the angle of the third displacement (mea- sured from the positive x axis, with counter- clockwise positive within the limits of ?180 degrees to +180 degrees). Answer in units of degrees.

Explanation / Answer

  First displacement     s     = 15 cos 27 * i + 15 sin 27 j                                        = 13.36  i +6.809 j   Second displacmenet s ' =6.1 cos 142 i + 6.1 sin 142 j                                         = -4.806 i + 3.755 j    Here after third displacement it comes to initial position   Net displacment S = 0                we know S = s + s' + s"   From this third displacment s "      = S - ( s+ s')                                                      = 0 - [ (13.36  i +6.809 j )+(-4.806 i + 3.755 j) ]                                                      = -8.554  i -10.564 j magnitude of third displacment s " =  [(-8.554   ) 2+(-10.564 ) 2]                                                       = 13.592 m
    Let the third displacment makes an angle theta with negative x-axis                                     Then tan ( ) = 10.554 / 8.554                                                      = 50.97 0 Angle with positive x-axis                = -180 +                                                         = -180+50.970                                                           = 129.030 Angle with positive x-axis                = -180 +                                                         = -180+50.970                                                           = 129.030

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