If it takes 8 min and 20 s for sunlight to reach the Earth, the distance between the Earth and the Sun is ______. (The velocity of light is `3xx10^(8)ms^(-1)`)

Options

A. `5xx10^(10)m`
B. `10xx10^(10)m`
C. `15xx10^(10)m`
D. `20xx10^(10)m`

Explanation

To find the distance between the Earth and the Sun based on the time it takes for sunlight to reach Earth, we can follow these steps:

### Step 1: Convert time from minutes and seconds to seconds
The time taken for sunlight to reach Earth is given as 8 minutes and 20 seconds.

1. Convert 8 minutes to seconds:
\[ 8 \text{ minutes} = 8 \times 60 = 480 \text{ seconds} \]

2. Add the extra 20 seconds:
\[ \text{Total time in seconds} = 480 \text{ seconds} + 20 \text{ seconds} = 500 \text{ seconds} \]

### Step 2: Use the speed of light to calculate distance
The speed of light is given as \(3 \times 10^8 \text{ m/s}\).

3. Use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

4. Substitute the values into the formula:
\[ \text{Distance} = (3 \times 10^8 \text{ m/s}) \times (500 \text{ seconds}) \]

### Step 3: Calculate the distance
5. Calculate the distance:
\[ \text{Distance} = 3 \times 10^8 \times 500 = 3 \times 500 \times 10^8 = 1500 \times 10^8 \text{ meters} \]

6. Convert \(1500 \times 10^8\) to scientific notation:
\[ 1500 = 1.5 \times 10^3 \quad \text{so} \quad 1500 \times 10^8 = 1.5 \times 10^{3 + 8} = 1.5 \times 10^{11} \text{ meters} \]

### Final Answer
The distance between the Earth and the Sun is approximately:
\[ \text{Distance} = 1.5 \times 10^{11} \text{ meters} \]

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