Sure! Let's tackle this problem step by step.
We need to convert the given speed of 212 feet per hour into different units: centimeters per second (cm/s) and meters per second (m/s).
### Part (a): Converting [tex]\(212 \text{ ft/hr}\)[/tex] to [tex]\( \text{cm/s} \)[/tex]
1. Understand the conversion factors:
- 1 foot = 30.48 centimeters
- 1 hour = 3600 seconds
2. Convert feet to centimeters:
- First, find how many centimeters are in 212 feet:
[tex]\[
212 \text{ feet} \times 30.48 \text{ cm/foot} = 6461.76 \text{ cm/hr}
\][/tex]
3. Convert from hours to seconds:
- We know that there are 3600 seconds in an hour, so to convert [tex]\( \text{cm/hr} \)[/tex] to [tex]\( \text{cm/s} \)[/tex]:
[tex]\[
\frac{6461.76 \text{ cm/hr}}{3600 \text{ seconds/hr}} = 1.7949333333333335 \text{ cm/s}
\][/tex]
### Part (b): Converting [tex]\(212 \text{ ft/hr}\)[/tex] to [tex]\( \text{m/s} \)[/tex]
1. Understand the conversion factors:
- 1 foot = 0.3048 meters
- 1 hour = 3600 seconds
2. Convert feet to meters:
- First, find how many meters are in 212 feet:
[tex]\[
212 \text{ feet} \times 0.3048 \text{ meters/foot} = 64.646016 \text{ meters/hr}
\][/tex]
3. Convert from hours to seconds:
- To convert [tex]\( \text{meters/hr} \)[/tex] to [tex]\( \text{m/s} \)[/tex]:
[tex]\[
\frac{64.646016 \text{ meters/hr}}{3600 \text{ seconds/hr}} = 0.017949333333333335 \text{ m/s}
\][/tex]
### Summary
- [tex]\( 212 \text{ ft/hr} \)[/tex] converts to:
- [tex]\( 1.7949333333333335 \text{ cm/s} \)[/tex]
- [tex]\( 0.017949333333333335 \text{ m/s} \)[/tex]
By following these steps, we have successfully converted the speed from feet per hour to both centimeters per second and meters per second.
