On an open ground , a motorist follows a track that turns to his left by an angle of `60^(@)` after every 500 m. Starting from a given turn , specify the displacement of of the motorist at the third , sixth and eighth turn . Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

Explanation

Displacement of magnitude 1 km and direction `60^(@)` with the initial direction , total path length = 1.5km (third turn), null displacement vector , path length = 3 km (sixth turn), 866 `m.30^(@)`, 4 km (eight turn)