Final answer:
The bus's resultant displacement is 5.09 km at an angle of 29.5° north of west.
Step-by-step explanation:
To find the bus's resultant displacement, we need to break down the given displacements into their east and north components.
First, 3 km east results in an east displacement of 3 km and a north displacement of 0 km.
Next, 5 km at 45° NE can be broken down into an east displacement of (5 km)(cos 45°) and a north displacement of (5 km)(sin 45°).
Similarly, 4 km at 20° NW can be broken down into an east displacement of (4 km)(cos 20°) and a north displacement of -(4 km)(sin 20°) since it is in the opposite direction.
Finally, 2 km south results in a north displacement of -2 km and an east displacement of 0 km.
Adding up all the east and north displacements, we find that the resultant displacement of the bus is 5.09 km at an angle of 29.5° north of west.