The speed of light is 300 million meters per second. What is the speed of light measured in miles per hour? (Round your answer to the nearest million miles per hour.) How long does it take light to travel the distance of 142 million miles from the sun to Mars? (Round your answer to the nearest minute
The Correct Answer and Explanation is:
. Speed of Light in Miles per Hour
Given that the speed of light is 300 million meters per second, we can convert this to miles per hour using the following steps:
Conversion Factors:
- 1 mile = 1,609.34 meters
- 1 hour = 3,600 seconds
Step 1: Convert meters to miles
To convert 300 million meters to miles: 300,000,000 meters×(1 mile1,609.34 meters)=186,411.36 miles300,000,000 \, \text{meters} \times \left( \frac{1 \, \text{mile}}{1,609.34 \, \text{meters}} \right) = 186,411.36 \, \text{miles}300,000,000meters×(1,609.34meters1mile)=186,411.36miles
So, the speed of light is approximately 186,411.36 miles per second.
Step 2: Convert seconds to hours
Now, to convert this speed from miles per second to miles per hour, multiply by the number of seconds in an hour: 186,411.36 miles/second×3,600 seconds/hour=670,879,000 miles/hour186,411.36 \, \text{miles/second} \times 3,600 \, \text{seconds/hour} = 670,879,000 \, \text{miles/hour}186,411.36miles/second×3,600seconds/hour=670,879,000miles/hour
Rounding this to the nearest million miles per hour: Speed of light≈671,000,000 miles/hour\text{Speed of light} \approx 671,000,000 \, \text{miles/hour}Speed of light≈671,000,000miles/hour
2. Time for Light to Travel from the Sun to Mars
The distance from the Sun to Mars is 142 million miles. To calculate how long it takes light to travel this distance, we use the formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}Time=SpeedDistance
where:
- Distance = 142 million miles
- Speed = 671 million miles per hour (from the previous calculation)
Substitute the values: Time=142,000,000 miles671,000,000 miles/hour≈0.211 hours\text{Time} = \frac{142,000,000 \, \text{miles}}{671,000,000 \, \text{miles/hour}} \approx 0.211 \, \text{hours}Time=671,000,000miles/hour142,000,000miles≈0.211hours
Convert hours to minutes by multiplying by 60: 0.211 hours×60 minutes/hour≈12.66 minutes0.211 \, \text{hours} \times 60 \, \text{minutes/hour} \approx 12.66 \, \text{minutes}0.211hours×60minutes/hour≈12.66minutes
Rounding this to the nearest minute: Time≈13 minutes\text{Time} \approx 13 \, \text{minutes}Time≈13minutes
Final Answers:
- Speed of light: 671 million miles per hour
- Time to travel from the Sun to Mars: 13 minutes
