In space communication, the information can be passed from one place to another at a distance of 100km in

Options

A. 1 s
B. 0.5 s
C. 0.003s
D. `3.3 xx 10^(-4)` sec

Answer

To solve the problem of how long it takes for information to be transmitted over a distance of 100 km in space communication, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Distance**:
The distance given in the problem is 100 km. We need to convert this distance into meters for consistency with the speed of light.
\[ d = 100 \text{ km} = 100 \times 10^3 \text{ m} = 100000 \text{ m} \]

2. **Identify the Speed of Light**:
In space communication, information is transmitted using electromagnetic waves (like radio waves), which travel at the speed of light. The speed of light (c) is approximately:
\[ c = 3 \times 10^8 \text{ m/s} \]

3. **Use the Formula for Time**:
The time taken (t) to transmit information can be calculated using the formula:
\[ t = \frac{d}{c} \]
where \(d\) is the distance and \(c\) is the speed of light.

4. **Substitute the Values**:
Now, we can substitute the values we have into the formula:
\[ t = \frac{100 \times 10^3 \text{ m}}{3 \times 10^8 \text{ m/s}} \]

5. **Calculate the Time**:
Performing the calculation:
\[ t = \frac{100000}{300000000} = \frac{1}{3000} \text{ seconds} \]
Converting this to scientific notation:
\[ t = 3.33 \times 10^{-4} \text{ seconds} \]

6. **Conclusion**:
Therefore, the time taken for information to be passed from one place to another at a distance of 100 km is:
\[ t \approx 3.33 \times 10^{-4} \text{ seconds} \]

### Final Answer:
The time taken for information to be transmitted over a distance of 100 km in space communication is approximately \(3.33 \times 10^{-4}\) seconds.

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