A light-year is the distance light travels in one year (at speed = 2.998 x 10 8 m/s). How many meters are there in 1.00 light-year?

Hey, everyone in this problem, we're told that the earth's circumference at the equator is approximately 40,075 kilometers. And we're asked how many centimeters are there in the earth's equatorial circumference? They were given four answer choices all in centimeters, all have 4.0075 multiplied by 10 to some exponent. The only thing that's different is that exponent. So for a, the exponent is nine for B, it's four for C, it's 15 and for D it's six. So in this problem, we're given the equatorial circumference in kilometers, we wanna find it in centimeters. So we're simply converting our units. So let's start with what we were given. We have 40,000 and 75 kilometers and let's first convert to meters. OK. Converting from kilometers to meters. That's a little simpler. That's standard. So we're gonna do that first, then we can go from meters to centimeters. Now, we have kilometers in the numerator. We wanna get rid of that. So we're gonna multiply by something that has kilometers in the denominator. Now recall that we have 1000 m per every kilometer. So we're gonna multiply it by 1000 m divided by one kilometer, the unit of kilometer will divide up and we're gonna be left with the unit of meters. And now we're gonna do the same thing but to go to centimeters, we have meters in the numerator, we wanna get rid of that. So we're gonna multiply by something with meters in the denominator and we want centimeters in the numerator. We know that there are 100 centimeters in every meter. So we multiply by 100 centimeters divided by 1 m. The unit of meters divides out and what we essentially have is 40,075 multiplied by 1000, multiplied by 100 centimeters. And this is gonna be 4.0075 multiplied by 10 to the exponent or that's that first value, then we're multiplying by 10 to the exponent three. OK. That's our 1000. Then we're multiplying by 10 to the exponent two. That's our 100 that's all in centimeters. And if we combine all of those exponents together, we get 4.0075 multiplied by 10 to the exponent nine centimeters. Hm. So that is our equatorial circumference in centimeters, a lot of centimeters. If we compare this to our answer choices, we can see that this corresponds with answer choice A that's it for this one. Thanks everyone for watching. See you in the next video.

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1. Intro to Physics Units

Unit Conversions

Physics

1. Intro to Physics Units

Unit Conversions

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Problem 25a

Textbook Question

A light-year is the distance light travels in one year (at speed = 2.998 x 10⁸ m/s). How many meters are there in 1.00 light-year?

Verified step by step guidance

Understand the problem: A light-year is the distance light travels in one year. To find the distance in meters, we need to calculate the product of the speed of light and the time duration of one year in seconds.

Convert the time duration of one year into seconds. Use the fact that 1 year = 365.25 days (accounting for leap years), 1 day = 24 hours, 1 hour = 60 minutes, and 1 minute = 60 seconds. Multiply these values to find the total seconds in a year.

Write the formula for distance: \( d = v \cdot t \), where \( d \) is the distance, \( v \) is the speed of light (\( 2.998 \times 10^8 \ \text{m/s} \)), and \( t \) is the time in seconds calculated in the previous step.

Substitute the values of \( v \) and \( t \) into the formula. Perform the multiplication to determine the distance in meters.

Express the final result in scientific notation to maintain clarity and precision, as the value will be very large.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Speed of Light

The speed of light in a vacuum is approximately 299,792,458 meters per second (or about 3.00 x 10^8 m/s). This constant speed is fundamental in physics, particularly in the theory of relativity, and serves as a universal speed limit for all matter and information in the universe.

Distance Calculation

To calculate the distance light travels in one year, one must multiply the speed of light by the number of seconds in a year. There are 31,536,000 seconds in a year (60 seconds per minute, 60 minutes per hour, 24 hours per day, and 365 days per year), making this calculation essential for determining distances in astronomical terms.

Light-Year

A light-year is a unit of distance that represents how far light travels in one year. It is commonly used in astronomy to express vast distances between celestial objects, with one light-year equating to approximately 9.461 trillion kilometers or about 5.879 trillion miles.

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