An old man moves on a semi-circular track of radius 7 km during a morning walk. If he starts at one end of the truck and reaches at the other end, the distance and displacement of the person are :

Options

A. 20 km, 7 km
B. 22km, 14km
C. 14km, 7km
D. All of these

Answer

To solve the problem of the old man walking on a semi-circular track of radius 7 km, we need to calculate both the distance traveled and the displacement. Here’s a step-by-step solution:

### Step 1: Understand the Track
The old man is walking on a semi-circular track, which means he starts at one end of the semi-circle and walks to the other end.

### Step 2: Calculate the Distance
The distance traveled by the old man is the length of the semi-circular path. The formula for the circumference of a full circle is given by:
\[ \text{Circumference} = 2\pi r \]
Since he is walking on a semi-circle, the distance he travels is half of the circumference:
\[ \text{Distance} = \frac{1}{2} \times 2\pi r = \pi r \]
Given that the radius \( r = 7 \) km, we can substitute this value into the equation:
\[ \text{Distance} = \pi \times 7 \]
Using \( \pi \approx \frac{22}{7} \):
\[ \text{Distance} = \frac{22}{7} \times 7 = 22 \text{ km} \]

### Step 3: Calculate the Displacement
Displacement is defined as the shortest distance from the initial position to the final position. In this case, the shortest path from point A (starting point) to point B (ending point) is a straight line across the diameter of the semi-circle.

The diameter \( d \) can be calculated as:
\[ d = 2r \]
Substituting the radius:
\[ d = 2 \times 7 = 14 \text{ km} \]
Thus, the displacement is 14 km.

### Final Results
- **Distance traveled**: 22 km
- **Displacement**: 14 km