Question

A person travels on a semi-circular track of radius 50 m during a morning walk. If he starts from one end of the track and reaches the other end, calculate the distance traveled and displacement of the person.

Answer 1

Question:

A person travels on a semi-circular track of radius 50 m during a morning walk. If he starts from one end of the track and reaches the other end, calculate the distance travelled and displacement of the person.

Given:

• A person travels on a semi-circular track of radius 50 m
• He starts from one end of the track and reaches the other end

To Find:

• Distance travelled by the person.
• Displacement of the person.

Concept:

Here, we are given that a person travels on a track that's semi-circular and also we are given its radius. He starts his morning walk from one end of track and reaches it's other end. We have to find the Distance travelled by the person and displacement of the person. For finding the distance travelled by person we need to find Perimeter of Semi-circular track. Now, we know that Displacement is the shortest distance between starting point and ending point. In Semicircle the shortest distance between starting and ending point is it's Diameter. So, Displacement of the person would be calculated as diameter of the Semicircle.

______________________________________

★ Formula Used:

$\nrightarrow\rm{Perimeter\: of\: Semicircle=\pi \times r}$

$\nrightarrow\rm{Displacement=2\times r}$

• r is Radius of semi-circle

______________________________________

Solution:

Let's first find out the Distance travelled by the person.

» Radius of semi-circular track, r = 50 m

$\: \: \: \rightarrow\rm{Perimeter\: of\: Semicircle=\pi\ times r}$

• As distance travelled by person equals to perimeter of semi-circle::

$\: \: \: \rightarrow\rm{Distance\: travelled\: by\: Person=\pi\times r}$$\\ \: \: \: \rightarrow\rm{Distance\: travelled\: by\: Person=\large{\frac{22}{7}}\times 50}$

• Multiplying 22 by 50::

$\: \: \: \rightarrow\rm{Distance\: travelled\: by\: person=\large{\frac{1100}{7}}}$ $\\ \: \: \: \rightarrow\bold{Distance\: travelled\: by\: person=157.14}$

Hence, Distance travelled by person is 157.14 m

Now, Let's find Displacement of person.

$\: \: \:\implies\rm{Displacement=2\times r}$

$\: \: \:\implies\rm{Displacement=2\times 50}$ $\\ \: \: \: \implies\bold{Displacement=100}$

Hence, Displacement of person is 100 m

Required Answers: $\\ \: \: \: \hookrightarrow\color{purple}{\underline{\mathsf{Distance\: travelled\: by\: person\: is\: 157.14\: m}}}$

$\: \: \: \hookrightarrow\color{purple}{\underline{\mathsf{Displacement\: of\: person\: is\: 100\: m}}}$

Answer 2

Explanation:

pls mark as branliest answer