SOLUTION: The speed of light is 3.0 x 108 m/sec. The Earth is 1.5 x 1011 m from the Sun. How many seconds does it take for light to reach us from the Sun?

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Question 97623This question is from textbook The Physical Universe
: The speed of light is 3.0 x 108 m/sec. The Earth is 1.5 x 1011 m from the Sun. How many seconds does it take for light to reach us from the Sun? This question is from textbook The Physical Universe

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
The distance between the Earth and the Sun is 1.5+%2A+10%5E11 meters
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and the speed of light is 3%2A10%5E8 meters/second.
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To get the answer of seconds you need to have seconds in the numerator, not in the denominator
as you were given. So since 3%2A10%5E8 is the number of meters light travels in 1 second,
you put the 1 second in the numerator and the 3%2A10%5E8 meters in the denominator.
.
Therefore, you have the ratio:
.
%281+second%29%2F%28%283%2A10%5E8%29+meters%29
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Now to get rid of the units of meters in the denominator, you need to multiply this ratio
by the number of meters in a numerator ... so that the units of meters in the numerator cancel
the units of meters in the denominator of our ratio.
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The number of units for your numerator comes from the distance between the Earth and the Sun.
When you multiply the conversion ratio by this distance we get:
.
%28%281.5%2A10%5E11%29%28+meters%29+%2A+%281+second%29%29%2F%28%283%2A10%5E8%29+meters%29%29
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Note that the units of "meters" cancel:
.

.
and you are left with the numbers in the numerator and denominator plus the units of
second. So the problem reduces to:
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%281.5%2A10%5E11%29%2F%283.0+%2A10%5E8%29 seconds
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When you divide the 1.5 by the 3.0 you get 1/2 or 0.5. You divide the 10%5E11 by 10%5E8 by
simply subtracting the exponent in the term of the denominator from the exponent of the
term in the numerator (note that they are both base 10 so you can do this) and you get
10%5E%2811-8%29+=+10%5E3.
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Combining the two factors results in 0.5%2A10%5E3 seconds and multiplying the 0.5 times
the 10%5E3 is equivalent to multiplying 0.5 times 1000 (or taking half of 1000). This
results in 500 seconds as being the answer. (Since there are 60 seconds in a minute,
500 seconds divided by 60 is 8.3333. This means that when light leaves the Sun it takes
8.3333 minutes to reach the Earth.)
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So the answer to this problem is 500 seconds. Hope this helps. Study the way in which you
look at the units. Work backwards from the units to be in your answer. That will tell you
what needs to be in the denominator and what needs to be in the numerator so the units cancel
and you are left with just the units you want in your answer. Takes practice, but once
you get it, it's very helpful in doing conversions of units.
.