The distance from the Earth to the moon is 239,000 miles. The distance from the Earth to the moon is 385000 km. Given that light travels at 3.00 x 10 m/s how many minutes does it take for light to travel to the moon?
The Correct Answer and Explanation is:
Let’s solve this step-by-step:
Given:
- Distance Earth to Moon:
- 239,000 miles
- 385,000 km
- Speed of light: $3.00 \times 10^8$ meters/second (I assume you meant $10^8$ m/s, since $10$ m/s is too slow for light)
Step 1: Convert distance to meters
We need to use consistent units, so convert the distance from kilometers to meters (since the speed of light is in meters per second).
- $1 \text{ km} = 1,000 \text{ meters}$
- Distance to moon = $385,000 \text{ km} \times 1,000 = 385,000,000 \text{ meters} $ (or $3.85 \times 10^8$ meters)
Step 2: Calculate time in seconds
Time $t$ is distance divided by speed:
$$
t = \frac{d}{v}
$$
Where:
- $d = 3.85 \times 10^8 \, m$
- $v = 3.00 \times 10^8 \, m/s$
So,
$$
t = \frac{3.85 \times 10^8}{3.00 \times 10^8} = 1.2833 \text{ seconds}
$$
Step 3: Convert seconds to minutes
Since $1 \text{ minute} = 60 \text{ seconds}$, convert seconds to minutes:
$$
t = \frac{1.2833}{60} = 0.02139 \text{ minutes}
$$
Final answer:
It takes approximately 1.28 seconds or about 0.021 minutes for light to travel from the Earth to the Moon.
Explanation:
The speed of light in vacuum is a fundamental constant of nature, about $3.00 \times 10^8$ meters per second. Light travels incredibly fast, so even vast distances like the distance between the Earth and the Moon can be traversed in a very short time.
The Earth-Moon distance is given both in miles and kilometers. For calculation with the speed of light in meters per second, it’s easiest to convert the distance to meters. Given 385,000 kilometers, converting to meters is straightforward by multiplying by 1,000 (since 1 km = 1,000 m). This yields $3.85 \times 10^8$ meters.
Dividing this distance by the speed of light gives the time it takes light to travel from the Earth to the Moon in seconds. The result is about 1.28 seconds, which confirms why astronauts on the Moon and mission control on Earth experience only a slight delay in communication signals traveling at light speed.
Finally, converting seconds to minutes shows that the time is about 0.021 minutes — a fraction of a minute but important when considering the speed and distance involved.
This short time interval is crucial in space communication and navigation, demonstrating both the vastness of space and the incredible speed at which light travels. It also provides a sense of scale — while 239,000 miles or 385,000 km is huge on Earth, light covers it in just over a second.
If you’d like, I can also calculate the time using miles and convert accordingly, but since the speed of light is typically in meters per second, kilometers to meters is more direct and less error-prone.