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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
On an open ground, a motorist follows a track that turns to his left by an angle of 60after 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 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

P R space equals space square root of PQ squared plus QR squared plus 2 left parenthesis PQ right parenthesis left parenthesis QR right parenthesis space cos space 60 to the power of straight o end root space

space space space space space space equals space square root of left parenthesis 500 right parenthesis squared plus left parenthesis 500 right parenthesis squared plus left parenthesis 2 cross times 500 cross times 500 cross times c o s space 60 to the power of o end root space

space space space space space space equals square root of 250000 plus 250000 plus left parenthesis 500000 cross times 1 half right parenthesis end root space
space space space space space space equals space 866.03 space m space

beta space equals space t a n to the power of negative 1 end exponent space open parentheses fraction numerator 500 space s i n space 60 to the power of o over denominator 500 space plus space 500 space c o s space 60 to the power of o end fraction close parentheses space equals space 30 to the power of o

 
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. 

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