Answer:
240.0 m at 57.2° south of west
Step-by-step explanation:
Take east to be the +x direction and north to be the +y direction.
The x component of the displacement is the sum of the individual x components.
x = 100 + 0 − 150 cos 30 − 200 cos 60
x = -75√3
x ≈ -129.9 m
Similarly, the y component of the displacement is the sum of the individual y components.
y = 0 − 300 − 150 sin 30 + 200 sin 60
y = -375 + 100√3
y ≈ -201.8 m
The magnitude of the displacement is found with Pythagorean theorem:
d² = x² + y²
d² = (-129.9)² + (-201.8)²
d = 240.0 m
The direction of the displacement is:
tan θ = y/x
tan θ = -201.8 / -129.9
θ = 57.2° below the -x axis
Therefore, the displacement is 240.0 m at 57.2° south of west.