Question

A circular track has a diameter of 200m when the athelete is on half way what will be the distance and displacement of the athelete

Answer 1

Let us assume that an athlete starts from point A to point B. Here it covers half of the revolution. If he return backs to it's initial point i.e. A then it covers the one complete revolution.

Given that, an athlete completes one round of a circular track of diameter 200 m.

We have to find the the distance and displacement of the athelete.

For one complete revolution:

Distance covered in one round = Circumference of circle.

{ Circumference of circle = 2πr }

So,

Distance covered in one round = 2πr

(diameter is 200 m so radius is 100 m)

= 2 × 22/7 × 100 = 4400/7m

For half revolution:

Distance covered by athele = 1/2 × 2πr

= 22/7 × 100 = 2200/7 m

Now,

Displacement is defined as the shortest distance between the initial and final points.

For one complete revolution:

Displacement of an athlete completes one round of a circular track is zero. As it's initial and final points are same.

Displacement of an athlete is 200 m.

For half revolution:

Displacement of an athlete is equal to it's diameter of circular track.

Displacement of an athlete is 200 m.

Answer 2

★ Given :

• A circular track has a diameter of 200m.
• Radius = 100 m

★ To Find :

We have to find the distance and displacement when athlete is on half way.

★ Explanation :

Firstly, we will calculate the distance of the athelete.

As, we have to calculate the distance of the circular track. So, we will calculate the circumference of circle.

$\Large{\star{\underline{\boxed{\sf{Circumference = 2\pi r}}}}}$

A.T.Q

We have to calculate the distance when athlete completed half track.

So, we will decide circumference by 2.

$\sf{\dashrightarrow Distance = \dfrac{Circumference}{2}} \\ \\ \sf{\dashrightarrow Distance = \dfrac{2 \pi r}{2}} \\ \\ \sf{\dashrightarrow Distance = \pi r} \\ \\ \sf{\dashrightarrow Distance = 3.14 \times 100} \\ \\ \sf{\dashrightarrow Distance = 314} \\ \\ \large{\star{\underline{\boxed{\sf{Distance = 314 \: m}}}}}$

$\rule{200}{2}$

Now,

We will find the displacement.

As, the Displacement is the shortest distance and athelete covered half track.

Then, Displacement must be the diameter of the circular track.

So, Displacement = 200 m

$\large{\star{\underline{\boxed{\sf{Displacement = 200 \: m}}}}}$

$\rule{400}{4}$