Anjali fires two bullets from the same place at an interval of 6 minutes but Bhagwat sitting in a car approaching the place of firing herts the second fire 5 minutes 32 seconds after the first firing.What is the speed of car if the speed of sound is 332 m/s?

Options

A. 56 m/s
B. 102 m/s
C. 28 m/s
D. 32 m/s

Answer

To solve the problem step by step, we need to analyze the information given and apply the concepts of time, speed, and distance.

### Step 1: Understand the problem
Anjali fires two bullets at an interval of 6 minutes. Bhagwat, who is in a car approaching the firing point, hears the second bullet 5 minutes and 32 seconds after he hears the first bullet. The speed of sound is given as 332 m/s.

### Step 2: Convert the time intervals into seconds
- The interval between the two bullet firings is 6 minutes, which is equal to:
\[ 6 \text{ minutes} = 6 \times 60 = 360 \text{ seconds} \]
- The time Bhagwat hears the second bullet after the first is 5 minutes and 32 seconds, which is equal to:
\[ 5 \text{ minutes} + 32 \text{ seconds} = 5 \times 60 + 32 = 332 \text{ seconds} \]

### Step 3: Determine the time difference
- If Bhagwat had not moved, he would have heard the second bullet 360 seconds after the first. However, he hears it in 332 seconds, which means he saved:
\[ 360 \text{ seconds} - 332 \text{ seconds} = 28 \text{ seconds} \]

### Step 4: Calculate the time taken by sound to travel the distance
- The sound takes 6 minutes (360 seconds) to travel from the firing point to Bhagwat when he is stationary.
- The sound takes 28 seconds less time when Bhagwat is moving, meaning the sound takes:
\[ 360 \text{ seconds} - 28 \text{ seconds} = 332 \text{ seconds} \]

### Step 5: Calculate the distance traveled by sound
- The distance (D) that the sound travels in 360 seconds at a speed of 332 m/s is:
\[ D = \text{Speed} \times \text{Time} = 332 \text{ m/s} \times 360 \text{ seconds} = 119520 \text{ meters} \]

### Step 6: Calculate the distance the sound travels in 28 seconds
- The distance the sound travels in 28 seconds is:
\[ D_{sound} = 332 \text{ m/s} \times 28 \text{ seconds} = 9296 \text{ meters} \]

### Step 7: Calculate the speed of Bhagwat's car
- The distance Bhagwat's car travels in the time saved (28 seconds) is the same as the distance the sound would have traveled in that time. Thus, the speed of the car (V) can be calculated as:
\[ V = \frac{D_{sound}}{t_{saved}} = \frac{9296 \text{ meters}}{28 \text{ seconds}} = 332 \text{ m/s} \]

### Step 8: Finalize the answer
- The speed of Bhagwat's car is:
\[ \text{Speed of car} = 332 \text{ m/s} \]

### Conclusion
The speed of Bhagwat's car is **332 m/s**.