A boy is cycling around a circular path of a radius of 70 m. What is the distance and
displacement of the boy when he completes half a revolution?
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A boy is cycling around a circular path of a radius of 70 m. What is the distance and
displacement of the boy when he completes half a revolution?
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Explanation:
As per the provided information in the given question, we have:
We are asked to calculate distance travelled and displacement of the boy when he completes half a revolution.
Let us say that the body starts from A. Therefore, after completing half a revolution, it will come to B.
★ Calculating the distance travelled :
Distance is defined as the total path covered by the body. Here, total distance covered will be half pf the circumference of the circular path,
[tex] \\ \twoheadrightarrow \sf { Distance = \dfrac{Circumference}{2} } \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { Distance = \dfrac{2\pi r}{2} } \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { Distance = \pi r} \\ [/tex]
Substituting the values of radius, that is 70 m.
[tex] \\ \twoheadrightarrow \sf { Distance =\Bigg \{ \dfrac{22}{7} \times 70 \Bigg \} \; m} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { Distance =\Bigg \{ 22 \times 10 \Bigg \} \; m} \\ [/tex]
[tex] \\ \twoheadrightarrow \bf \underline{ Distance =220\; m} \\ [/tex]
Therefore, distance travelled by the body is 220 m.
★ Calculating the displacement :
Displacement is the shortest distance from initial position to final position. Here, initial position is A and final position is B. The shortest distance from A to B is AB, which can be considered as the diameter of the circular path.
[tex] \\ \twoheadrightarrow \sf { Displacement = Diameter} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { Displacement = 2 \times Radius} \\ [/tex]
[tex] \\ \twoheadrightarrow \sf { Displacement = (2 \times 70 ) \; m} \\ [/tex]
[tex] \\ \twoheadrightarrow \bf\underline { Displacement = 140\; m} \\ [/tex]
Therefore, displacement is 140 m.