To convert a speed from miles per hour (mi/h) to meters per second (m/s), we can follow these steps:
1. Identify the given speed:
The given speed is [tex]\(55\)[/tex] miles per hour (mi/h).
2. Identify the conversion factors:
- 1 mile (mi) is equivalent to [tex]\(1609\)[/tex] meters (m).
- 1 hour (h) is equivalent to [tex]\(3600\)[/tex] seconds (s).
3. Convert miles to meters:
We need to convert the speed from miles to meters. Since 1 mile is [tex]\(1609\)[/tex] meters, we multiply the speed in miles per hour by [tex]\(1609\)[/tex] to convert it to meters per hour (m/h):
[tex]\[
55 \text{ mi/h} \times 1609 \text{ m/mi} = 88495 \text{ m/h}
\][/tex]
4. Convert hours to seconds:
Now, we need to convert the speed from meters per hour to meters per second. Since 1 hour is [tex]\(3600\)[/tex] seconds, we divide the speed in meters per hour by [tex]\(3600\)[/tex] to convert it to meters per second (m/s):
[tex]\[
\frac{88495 \text{ m/h}}{3600 \text{ s/h}} \approx 24.581944444444446 \text{ m/s}
\][/tex]
Therefore, [tex]\(55\)[/tex] miles per hour is approximately [tex]\(24.581944444444446\)[/tex] meters per second.
Among the given options:
- [tex]\(25 \text{ m/s}\)[/tex]
- [tex]\(49 \text{ m/s}\)[/tex]
- [tex]\(90 \text{ m/s}\)[/tex]
- [tex]\(120 \text{ m/s}\)[/tex]
The closest to our calculated value of [tex]\(24.581944444444446 \text{ m/s}\)[/tex] is [tex]\(25 \text{ m/s}\)[/tex].
Thus, [tex]\(55\)[/tex] miles per hour is approximately [tex]\(25 \text{ m/s}\)[/tex].
