- Question Answer
- On an open ground a motorist follows a track that turns to his left by an angle
. On an open ground a motorist follows a track that turns to his left by an angle
6 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.
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 A.
The motorist takes the third turn at D.
Magnitude of displacement =AD=BC+EF=500+500=1000m
Total path length =AB+BC+CD=500+500+500=1500m
The motorist takes the sixth turn at point A, which is the starting point.
Magnitude of displacement =0 Total path length =6AB =6×500=3000m
The motorist takes the eight turn at point C
The magnitude of displacement =AC From triangle law,
the magnitude of displacement is 866.03m at an angle of 30 with AC.
It means AC makes an angle 30 with the initial direction.
Total path length =8×500=4000m.
Hence, total path length is 4000m.