Question

3. A person running around a circular
park covers 3/4th of its
journey. If radius of the circular park is 50 m then find the
distance travelled and displacement of the body.​

Answer 1

Answer:

Distance = 235.5 m

Displacement = 50√2 m

Explanation:

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

• A person running around a circular park covers 3/4th of its journey.
• Radius of the park is 50 m.

Consider the provided figure in the attachment.

Suppose the body starts from A. So, after covering 3/4th of the park, he'll come to B.

Calculating distance travelled :

Distance is the total path covered by the body. Here, the person covers 3/4th of the circumference or the boundary of the park.

⇒ Distance = $\sf \dfrac {3}{4}$ × Circumference

⇒ Distance = $\sf \dfrac {3}{4}$ × 2πr

⇒ Distance = $\sf \dfrac {3}{4}$ × (2 × 3.14 × 50) m

⇒ Distance = $\sf \dfrac {3}{4}$ × 314 m

⇒ Distance = 3 × 78.5 m

⇒ Distance = 235.5 m

∴ Distance covered is 235.5 m.

Calculating displacement :

Displacement is the shortest distance form initial to final position of the body. Here, initial position is A and final position is B. The shortest path from A to B is AB. Now, consider the quarter of the circle AOB. AO and BO are the radii of the circle.

Now, by using Pythagoras property :-

⇒ (AB)² = (AO)² + (BO)²

⇒ (AB)² = (50 m)² + (50 m)²

⇒ (AB)² = 2500 m² + 2500 m²

⇒ (AB)² = 5000 m²

⇒ AB = √(5000 m²)

⇒ AB = 50√2 m

⇒ Displacement = 50√2 m

∴ Displacement of the person is 50√2 m.