Convert 352 lightyears/century into feet/second.
Convert lightyears to feet.
A lightyear is the distance light travels in one year. The speed of light is approximately \(299,792,458\) meters per second.
To find the distance in one year:
\[
299,792,458 \, \text{m/s} \times 60 \, \text{s/min} \times 60 \, \text{min/hr} \times 24 \, \text{hr/day} \times 365.25 \, \text{days/year}
\]
This equals approximately \(9.461 \times 10^{15}\) meters.
Convert meters to feet (1 meter = 3.28084 feet):
\[
9.461 \times 10^{15} \, \text{meters} \times 3.28084 \, \text{feet/meter} \approx 3.104 \times 10^{16} \, \text{feet}
\]
Thus, 1 lightyear is approximately \(3.104 \times 10^{16}\) feet.
Calculate feet per century.
Given 352 lightyears per century:
\[
352 \, \text{lightyears/century} \times 3.104 \times 10^{16} \, \text{feet/lightyear} \approx 1.093 \times 10^{19} \, \text{feet/century}
\]
Convert feet per century to feet per second.
There are \(100\) years in a century, \(365.25\) days in a year, \(24\) hours in a day, \(60\) minutes in an hour, and \(60\) seconds in a minute.
Calculate the total seconds in a century:
\[
100 \, \text{years} \times 365.25 \, \text{days/year} \times 24 \, \text{hours/day} \times 60 \, \text{minutes/hour} \times 60 \, \text{seconds/minute}
\]
This equals approximately \(3.15576 \times 10^9\) seconds.
Now, convert feet per century to feet per second:
\[
\frac{1.093 \times 10^{19} \, \text{feet/century}}{3.15576 \times 10^9 \, \text{seconds/century}} \approx 3.46 \times 10^9 \, \text{feet/second}
\]
\(\boxed{3.46 \times 10^9 \, \text{feet/second}}\)
\(\boxed{3.46 \times 10^9 \, \text{feet/second}}\)
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