A car approaches a hill with constant speed. When it is at a distance of 0.96 km from the hill, it blows horn whose echo is heard by the driver 6 seconds later. If the speed of sound in air is 300 m/s, calculate the speed of the car.

Options

A. 100 m/s
B. 20 m/s
C. 50 m/s
D. 70 m/s

Explanation

To solve the problem, we need to calculate the speed of the car based on the information given about the echo of the horn. Here’s a step-by-step solution:

### Step 1: Understand the situation
The car is at a distance of 0.96 km (or 960 meters) from the hill when it blows the horn. The echo of the horn is heard by the driver 6 seconds later. The speed of sound in air is given as 300 m/s.

### Step 2: Calculate the total distance traveled by the sound
When the car blows the horn, the sound travels to the hill and then back to the car. Therefore, the total distance traveled by the sound is twice the distance to the hill:
\[ \text{Total distance} = 2 \times 960 \text{ m} = 1920 \text{ m} \]

### Step 3: Calculate the time taken for the sound to travel
The time taken for the sound to travel to the hill and back is given as 6 seconds. We can use the speed of sound to find the distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Using the speed of sound (300 m/s):
\[ 1920 \text{ m} = 300 \text{ m/s} \times 6 \text{ s} \]

### Step 4: Calculate the distance traveled by the car
During the 6 seconds, the car is also moving towards the hill. Let the speed of the car be \( V \) m/s. The distance traveled by the car in 6 seconds is:
\[ \text{Distance traveled by car} = V \times 6 \]

### Step 5: Set up the equation
Initially, the distance between the car and the hill is 960 m. After 6 seconds, the distance between the car and the hill will be:
\[ 960 \text{ m} - (V \times 6) \]
Since the sound travels to the hill and back, we can equate the distances:
\[ 960 - 6V + 960 = 1920 \]
This simplifies to:
\[ 960 - 6V = 0 \]

### Step 6: Solve for the speed of the car
Rearranging the equation gives:
\[ 6V = 960 \]
\[ V = \frac{960}{6} = 160 \text{ m/s} \]

### Step 7: Conclusion
The speed of the car is \( 160 \text{ m/s} \).