it is estimated that light travels 100 000 years to travel the full distance across our galaxy, the milky way. If light travels 3.0x10^8 m every second, how long is the Milky Way? (1year=3.2x10^7s)
distance (m) = speed (m/s) * time (s)
10^5 years * 3*10^8 m/s * 3.2*10^7 s/yr = 9.6*10^20 s
or, as is usually written, 100,000 light-years (duh)
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To solve this problem, we need to understand that the estimated time it takes for light to travel across the galaxy is given as 100,000 years. We have also been given the speed of light, which is 3.0x10^8 m/s, and the conversion factor from years to seconds, which is 1 year = 3.2x10^7 seconds.
We can start by calculating the total distance light travels across the Milky Way using the formula:
Distance = Speed x Time
First, let's convert the given time into seconds. Since 1 year is equal to 3.2x10^7 seconds, we can multiply the given time (100,000 years) by 3.2x10^7 to convert it into seconds:
Time = 100,000 years * 3.2x10^7 seconds/year
Next, we can plug the values into the formula:
Distance = 3.0x10^8 m/s * (100,000 years * 3.2x10^7 seconds/year)
Now, let's perform the multiplication:
Distance = 3.0x10^8 m/s * (3.2x10^7 seconds/year * 100,000 years)
We can simplify the calculation further:
Distance = 3.0x10^8 m/s * 3.2x10^7 seconds * 100,000
When multiplying scientific notation numbers, we add the exponents:
Distance = (3.0 * 3.2) * (10^8 * 10^7) * 100,000 m
Calculating the numbers outside of the exponential notation:
Distance = 9.6 * 10^15 * 100,000 m
Multiplying 9.6 by 100,000:
Distance = 960,000 * 10^15 m
Finally, we can write the answer in scientific notation:
Distance = 9.6x10^20 m
Therefore, the Milky Way is estimated to be approximately 9.6x10^20 meters long.