The path followed by the motorist is a regular hexagon with side 500 m, as shown in the given figure.
Let the motorist start from point P.
The motorist takes the third turn at S.
∴ Magnitude of displacement = PS = PV + VS = 500 + 500 = 1000 m
Total path length = PQ + QR + RS = 500 + 500 +500 = 1500 m
The motorist takes the sixth turn at point P, which is the starting point.
∴ Magnitude of displacement = 0
Total path length = PQ + QR + RS + ST + TU + UP
= 500 + 500 + 500 + 500 + 500 + 500
= 3000 m
The motorist takes the eight turn at point R.
∴ Magnitude of displacement = PR
Therefore, the magnitude of displacement is 866.03 m at an angle of 30° with PR.
This implies AC makes an angle 30° with the initial direction.
Total path length = 8 × 500 = 4000 m.