STARTING FROM ONE OF THE VERTICES OF A REGULAR HEXAGON , THE PARTICLE COVERS THE THREE SIDES OF THE REGULAR HEXAGON IN ORDER . WHAT IS DISPLACEMENT OF THE PARTICLE DURING THIS MOTION [GIVEN THAT THE SIDE OF THIS REGULAR HEXAGON IS 'a ' units.] ? *
Answers
Given : A particle covers the three sides of a regular hexagon of unit a
To Find : Displacement of particle
Solution:
Hexagon internal angle = 120°
Let say first side is along x axis
Then Horizontal Distance = a
Vertical Distance = 0
in 2nd side - Horizontal Distance = aCos60 = a/2
Vertical distance = asin60 = √3 a /2
in 3rd side - Horizontal Distance = aCos120 = -a/2
Vertical distance = asin120 = √3 a /2
Total Horizontal = a + a /2 - a /2 = a
Total Vertical = 0 + √3 a /2 + √3 a /2 = √3 a
Total Displacement = √a² + (√3 a)² = 2a
Displacement of particle during motion is 2a units
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