Question

an athlete completes one round of a circular diameter 200m in 40s.what will be the distance and displacement at the end of 2 mins 20s?

Answer 1

Answer:

Distance travelled = 2200 m

Displacement = 200 m (from A to B)

Explanation:

As per the provided information in the given question, we have :

• An athlete completes one round of a circular diameter 200m in 40s .

We are asked to calculate the distance and displacement at the end of 2 mins 20s.

Converting minutes in seconds :

→ 2 minutes 20 s

→ (2 × 60) + 20 seconds

→ 120 + 20 seconds

→ 140 seconds

Now, let us say that the body starts from point A.

So, according to the question, he covers 1 round is 40 s.

⇒ Time taken to cover one round = 40 s

So,

⇒ In one second it'll cover number of rounds = $\sf \dfrac{1}{40}$ round

Thus,

⇒ In 140 seconds it'll cover number of rounds = ($\sf \dfrac{1}{40}$ × 140) rounds

⇒ In 140 seconds it'll cover number of rounds = ($\sf \dfrac{1}{4}$ × 14) rounds

⇒ In 140 seconds it'll cover number of rounds = 3.5 rounds

So, 3.5 rounds will be covered by the athlete in 140 seconds.

Calculating distance travelled :

⇒ Distance travelled = Number of rounds in 140s × Distance covered in one round

• Distance covered in one round will be the perimeter of the circle.

⇒ Distance travelled = (3.5 × 2πr) m

⇒ Distance travelled = (3.5 × 2 × $\sf \dfrac{22}{7}$ × 100) m

• Since, the diameter is 200 m, the radius will be the half of the diameter.

⇒ Distance travelled = ($\sf \dfrac{35}{10}$ × 2 × $\sf \dfrac{22}{7}$ × 100) m

⇒ Distance travelled = (5 × 2 × 22 × 10) m

⇒ Distance travelled = 2200 m

∴ Distance travelled by the athlete is 2200 m .

$\rule{200}2$

Calculating displacement :

In order to find the displacement, we need to find its final position. Final position will be the position after 3.5 rounds.

After 3 rounds, it'll come back again to point A. Then, it cover 0.5 round or half round. That means, B (in the diagram) will be its finally position which is diagrammatically opposite to point A.

Displacement is the shortest distance from initial to final position. Here, initial position is A and final position is B. The shortest distance between two points is always a straight line. So, AB or diameter of the circular path is the displacement.

⇒ Diameter = 200 m (Given in the question)

⇒ Displacement = 200 m (Since, diameter is the displacement)

∴ Displacement of the athlete is 200m from A to B.

Answer 2

Answer:-

Figure:-

$\setlength{\unitlength}{.5in}\begin{picture}(0,0)\thicklines\put(0,0){\circle{1}}\qbezier(-0.5,0)(0.5,0)(0.5,0)\put(0,0.1){\sf 200m}\end{picture}$

• Diameter=200m
• Radius=Diameter/2=200/2=100m

Finding Displacement:-

• Here Displacement is equal to diameter

Hence Displacement=200m

$\rule{200}{3}$

Finding Circumference :-

$\boxed{\sf Circumference=2\pi r}$

$\\ \rm\longmapsto Circumference=2\dfrac{22}{7}\times 100$

$\\ \rm\longmapsto Circumference=\dfrac{4400}{7}$

$\\ \rm\longmapsto Circumference=628.5m$

Now

• Distance=628.5m
• Time=40s

Finding speed

$\boxed{\sf Speed=\dfrac{Distance}{Time}}$

$\\ \rm\longmapsto Speed=\dfrac{628.5}{40}$

$\\ \rm\longmapsto Speed=15.7m/s$

Finding Total time

$\\ \rm\longmapsto 2min\:20s$

$\\ \rm\longmapsto 2(60s)+20s$

$\\ \rm\longmapsto 120s+20s$

$\\ \rm\longmapsto 140s$

Finding Total rounds :-

• It takes 40s for 1round
• It will complete n rounds in 140s

$\\ \rm\longmapsto n=\dfrac{140}{40}$

$\\ \rm\longmapsto n=3.5$

Finding Distance:-

$\\ \rm\longmapsto Distance=Circumference\times n$

$\\ \rm\longmapsto Distance=628.5\times 3.5$

$\\ \rm\longmapsto Distance=2199.3m$

$\\ \rm\longmapsto Distance=2200m(Approx)$

$\\ \pmb{\rm\longmapsto Distance=2.2km}$