Question

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 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.​

Answer 1

okaY!

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

So After solving This You Got 4000m