To determine the speed of a satellite orbiting Earth in kilometers per second, given its speed in miles per hour, you can follow these steps:
1. Convert the speed from miles per hour to kilometers per hour:
- We know that 1 mile is approximately equal to 0.62 kilometers.
- Therefore, if the satellite is traveling at 17,000 miles per hour, we can convert this speed to kilometers per hour by multiplying by the conversion factor:
[tex]\[
17,000 \, \text{miles/hour} \times 0.62 \, \text{km/mile} = 10,540 \, \text{km/hour}
\][/tex]
2. Convert the speed from kilometers per hour to kilometers per second:
- There are 3,600 seconds in one hour.
- To convert the speed from kilometers per hour to kilometers per second, we divide the speed in kilometers per hour by the number of seconds in an hour:
[tex]\[
10,540 \, \text{km/hour} \div 3,600 \, \text{seconds/hour} \approx 2.9277777777777776 \, \text{km/second}
\][/tex]
3. Round the result to the appropriate number of significant figures:
- Considering the significant figures from the original speed of 17,000 miles/hour (2 significant figures), we round the result to 2 significant figures:
[tex]\[
2.9277777777777776 \, \text{km/second} \approx 2.9 \, \text{km/second}
\][/tex]
Therefore, the satellite's speed in the correct number of significant figures is approximately 2.9 km/s.
The correct answer is:
A. 2.9 km/s
