A person moves on a semi - circular track of radius radius 42 m during a morning walk. He starts at one end of the track and reaches the other end. Find the distance covered and the displacment of the person .

Answer

To solve the problem, we need to calculate both the distance covered by the person and the displacement. Here's a step-by-step breakdown:

### Step 1: Calculate the Distance Covered
The distance covered by the person walking on a semi-circular track can be calculated using the formula for the circumference of a circle. The formula for the circumference of a full circle is:

\[ C = 2\pi r \]

Since the person is walking on a semi-circular track, we take half of the circumference:

\[ \text{Distance} = \frac{1}{2} \times C = \frac{1}{2} \times 2\pi r = \pi r \]

Given that the radius \( r = 42 \) m, we can substitute this value into the equation:

\[ \text{Distance} = \pi \times 42 \]

Using \( \pi \approx \frac{22}{7} \):

\[ \text{Distance} = \frac{22}{7} \times 42 \]

Calculating this gives:

\[ \text{Distance} = \frac{22 \times 42}{7} = \frac{924}{7} = 132 \text{ m} \]

### Step 2: Calculate the Displacement
Displacement is defined as the shortest distance between the initial and final positions. In this case, the person starts at one end of the semi-circle and ends at the other end. The displacement will be the straight line distance across the diameter of the semi-circle.

The diameter \( d \) of the semi-circle is given by:

\[ d = 2r \]

Substituting the radius:

\[ d = 2 \times 42 = 84 \text{ m} \]

### Final Results
- **Distance Covered**: 132 m
- **Displacement**: 84 m