Question

A particle undergoes two displaments , measured from the positive x-axis, with counterclockwise positive.The first has a magnitude of 11 m and makes an angle of 88 with the positive x-axis. The resultant displacement has a magnitude of 6.8 m direceted at an angle of 115 from the positive x-axis.

Find the magnitude of the second displacement. Find the angle of the second displacement (measured from the positive x axis, with counterclockwise positive within the limits of -180 to +180)

Answer 1

Just convert the data to rectangular coordinates:

11 @ 88° = 0.0349,10.9933
6.8 @ 115V = -2.8738,6.1629

so, now you want (x,y) such that

0.0349+x = -2.8738
10.9933+y = 6.1629

Then convert that (x,y) back to polar avlues.