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 counter-clockwise positive. The first has a magnitude of 11 m and makes an angle of 67 degrees with the positive x axis. The resultant displacement has a magnitude of 10.1 m directed at an angle of 124 degrees 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 degrees to +180 degrees). (answer in units of degrees)

Explanation / Answer

resolving displacement on x-axis and y- axis: first displacement: x-axis = 11 cos 85* = 0.9587 m y-axis = - 11 sin 85 = 10.9581 m resultant : x-axis = -7 cos 67* = - 2.7351 m y-axis = - 7 sin 67 = - 6.4435 m second displacement : x- axis = -2.7351 - 0.9587 = - 3.6938 y-axis = - 6.4435 -10.9581 = -17.4016 second displacement = { (- 3.6938)^2 + (-17.4016)^2 }^0.5 = 17.7893 m..................ans tan theta = -17.4016 / - 3.6938 = 4.711 theta = 258.016*................................

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