Find the angle of the third displacement (measured from thepositive x axis, with

Question

Find the angle of the third displacement (measured from thepositive x axis, with counter clockwise positive within the limitsof -180 and +180) The First has a magnitide of 15m and makes an angle of36. The second has a magnitude of 6 and makes a angle of 146 After the third displacement the particle returns to itsinitial position I found the magnitude of the third displacement which is14.122. I just need to figure the angle of the third Find the angle of the third displacement (measured from thepositive x axis, with counter clockwise positive within the limitsof -180 and +180) The First has a magnitide of 15m and makes an angle of36. The second has a magnitude of 6 and makes a angle of 146 After the third displacement the particle returns to itsinitial position I found the magnitude of the third displacement which is14.122. I just need to figure the angle of the third

Explanation / Answer

first   + second + third = 0 . (15cos36 i   + 15sin36 j )  +   ( 6cos146 i + 6sin146 j)   +(x i     +   y j ) = 0 . So...     x =  -15cos36   -   6cos146  =    - 7.161 .           y =   -15sin36   - 6sin146 =    - 12.17 . This is where you got the magnitude, right?   [ 7.1612 + 12.172]1/2   =    14.12 . The angle can be found by .     tan   = y component/ x componet   =   - 12.17 / -7.161 .          = arctan(1.69975)   =     239.5degrees from x axis

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