Question

Displacement of a person moving from X to Y along a semi-circular path of radius r is \[200\;{\rm{m}}\].What is the distance travelled by him?

Answer 1

Hint:The above problem can be resolved using the concepts of kinematics. In kinematics, one can define the displacement across any given path by merely identifying the shortest length of the path to be covered to reach the final point. Moreover, in the problem, the semi-circular path is given with the magnitude of displacement. This distance covered along this semi-circular path is obtained by taking half the full circle's circumference value. And for this, the radius can be calculated by taking half of the displacement.

Complete step by step answer:
Given:
The displacement covered along the semi-circular path is, \[D = 200\;{\rm{m}}\].
Then the radius of the semi-circular path is,
\[r = \dfrac{D}{2}\]
And the distance travelled by the person is,
\[\begin{array}{l}
S = \dfrac{{2\pi r}}{2}\\
S = \pi r
\end{array}\]
Solve by substituting the values in above equation as,
\[\begin{array}{l}
S = \pi r\\
S = \pi \left( {\dfrac{D}{2}} \right)\\
S = \pi \left( {\dfrac{{200\;{\rm{m}}}}{2}} \right)\\
S = 100\pi \;{\rm{m}}
\end{array}\]
Therefore, the distance travelled by the person along the semi-circular path is \[100\pi \;{\rm{m}}\].

Note: To resolve the given problem, one must recall the definition of displacement. Whenever we talk about displacement, we always conclude for the smallest length of the path that an object or body is supposed to travel. On the other hand, the distance always means covering the total length of the whole journey. Therefore, it is often taken in the wrong way and misjudged while calculating the corresponding displacement values and distance.