The resultant displacement is 58.54 mm at an angle of 120.1° measured counter-clockwise from the positive x-axis.
Resultant Displacement Calculation:
Step 1: Resolve each displacement into rectangular components.
60mm in +y direction: (0, 60) mm
30mm in -x direction: (-30, 0) mm
40mm at 150°: (-40cos(150°), 40sin(150°)) = (-25.98, 34.64) mm
50mm at 240°: (-50cos(240°), 50sin(240°)) = (25.98, -43.60) mm
Step 2: Sum the horizontal and vertical components separately.
Horizontal: -30 - 25.98 + 25.98 = -30 mm
Vertical: 60 + 34.64 - 43.60 = 51.04 mm
Step 3: Calculate the magnitude of the resultant displacement.
Resultant displacement = √(-30)^2 + (51.04)^2 ≈ 58.54 mm
Step 4: Determine the direction of the resultant displacement.
arctangent (vertical component / horizontal component) = arctangent (51.04 / -30) ≈ -59.9°
Step 5: Adjust the direction for quadrant.
Since the horizontal component is negative and the vertical component is positive, the resultant displacement lies in the third quadrant. Therefore, add 180° to the calculated angle: -59.9° + 180° = 120.1°