The distance from the Earth to the Sun is about 93 million miles. If light travels at a speed of 2.998×10^8 m/s, how many minutes does it take for light from the Sun to reach the Earth? Enter only the number and the unit for the answer: 2.8×10^-8 min
The Correct Answer and Explanation is:
To calculate how long it takes for light from the Sun to reach the Earth, we need to consider the distance from the Earth to the Sun and the speed at which light travels.
Step 1: Convert distance to meters
The distance from the Earth to the Sun is approximately 93 million miles. First, we need to convert miles to meters.1 mile=1609.34 meters1 \, \text{mile} = 1609.34 \, \text{meters}1mile=1609.34meters93 million miles=93×106 miles93 \, \text{million miles} = 93 \times 10^6 \, \text{miles}93million miles=93×106miles93×106 miles×1609.34 meters/mile=1.496×1011 meters93 \times 10^6 \, \text{miles} \times 1609.34 \, \text{meters/mile} = 1.496 \times 10^{11} \, \text{meters}93×106miles×1609.34meters/mile=1.496×1011meters
Step 2: Use the speed of light
We are given that the speed of light is 2.998×108 m/s2.998 \times 10^8 \, \text{m/s}2.998×108m/s.
Step 3: Calculate time
Time can be calculated using the formula:Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}Time=SpeedDistance
Substituting the known values:Time=1.496×1011 meters2.998×108 m/s=499.6 seconds\text{Time} = \frac{1.496 \times 10^{11} \, \text{meters}}{2.998 \times 10^8 \, \text{m/s}} = 499.6 \, \text{seconds}Time=2.998×108m/s1.496×1011meters=499.6seconds
Step 4: Convert time from seconds to minutes
To convert seconds to minutes:Time in minutes=499.6 seconds60≈8.33 minutes\text{Time in minutes} = \frac{499.6 \, \text{seconds}}{60} \approx 8.33 \, \text{minutes}Time in minutes=60499.6seconds≈8.33minutes
Final Answer:
It takes approximately 8.33 minutes for light to travel from the Sun to the Earth.
