A radar is able to detect the reflected waves from an enemy's aeroplane after a time interval of $0.02 × 10^{-3}$ sec. If the velocity of the waves is $3 × 10^8$ m/s. The distance of the aeroplane from the Radar will be :

Question

Accepted Answer

To determine the distance of the aeroplane from the radar, we need to use the formula for calculating distance based on the time taken for a wave to travel to an object and back. The formula is:

$$ \text{Distance} = \frac{\text{Velocity} \times \text{Time}}{2} $$

This formula accounts for the fact that the time given is for the round trip of the radar waves (to the aeroplane and back), so we divide by 2 to find the one-way distance.

Given:
- Time interval for the round trip, $ t = 0.02 \times 10^{-3} $ seconds
- Velocity of the waves, $ v = 3 \times 10^8 $ m/s

Substitute these values into the formula:

$$ \text{Distance} = \frac{3 \times 10^8 \, \text{m/s} \times 0.02 \times 10^{-3} \, \text{s}}{2} $$

$$ \text{Distance} = \frac{3 \times 10^8 \times 0.00002}{2} $$

$$ \text{Distance} = \frac{6 \times 10^3}{2} $$

$$ \text{Distance} = 3 \times 10^3 \, \text{m} $$

$$ \text{Distance} = 3.0 \, \text{km} $$

Therefore, the distance of the aeroplane from the radar is 3.0 km, which corresponds to Option 3.

**Explanation for Other Options:**

1. **Option 1 (1.0 km):** This option is incorrect because the calculated distance is 3.0 km, not 1.0 km. The calculation clearly shows that the distance is three times this value.

2. **Option 2 (1.5 km):** This option is incorrect because it is half of the calculated distance. The formula and calculation demonstrate that the correct distance is 3.0 km.

3. **Option 4 (6.0 km):** This option is incorrect because it is double the calculated distance. The calculation shows that the correct distance is 3.0 km, not 6.0 km.

In conclusion, the correct answer is Option 3, as the calculation based on the given time and velocity of the radar waves accurately results in a distance of 3.0 km.