Consider east-west direction along x-axis with north being in positive x-direction.
Consider north-south direction along x-axis with north being in positive x-direction.
A = magnitude of displacement in south direction = 370 m
= x-component of A = 0 m
= y-component of A = - 370 m
B = magnitude of displacement in south-west direction = 410 m
= x-component of B = - 410 Cos45 = - 289.91 m
= y-component of B = - 410 Sin45 = - 289.91 m
C = magnitude of displacement in 28 deg east of north direction = 370 m
= x-component of C = 370 Sin28 = 173.7 m
= y-component of C = 370 Cos28 = 326.7 m
= x-component of D = ?
= y-component of D = ?
To return to starting position, the sum of individual displacements alng each axis must be zero.
+
+
+
= 0
0 - 289.91 + 173.7 +
= 0
= 116.21 m
+
+
+
= 0
- 370 - 289.91 + 326.7 +
= 0
= 333.21 m
magnitude of D is given using Pythagorean theorem as
magnitude = sqrt((
)² + (
)²)
magnitude = sqrt((116.21)² + (333.21)²) = 352.89 m
direction : tan⁻¹(333.21/116.21) = 70.8 deg