A particle undergoes two displacements. The first has a magnitude of 128 cm and

Question

A particle undergoes two displacements. The first has a magnitude of 128 cm and makes an angle of 113 degrees with the positive x axis. The resultant displacement has a magnitude of 180 cm and is directed at an angle of 39 degrees to the positive x axis. Find the magnitude of the second displacement. Answer in units of cm. And find the direction of the second displacement (with positive measured from counter clock-wise from the x axis, and between the limits of -180 degrees and 180 degrees). Answer in degrees.

Explanation / Answer

resultant=d1+d2=180(cos39+sin39) d1=128(cos113+sin113) d2=180(cos39i+sin39j)-128(cos113i+sin113j)=139.886i+113.277j+50i-117.82j d2=189.886i-4.543j ?=tan-1(-4.543/189.883) mag=189.942 ?=-1.37deg

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