on an open ground a motorist follows a track that turns to his left by an angle of 60 degree after every 500m.starting from a given turn specify the displacemet of the motorist at the third,sixth,and eight turn.compare the magnitude of the displacement with the total path length covered by the motorist in each case.
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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.
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