To convert miles per hour (mph) to feet per second (ft/s), we can use the following conversion factors:
- Miles to feet: There are 5280 feet in a mile.
- Hours to seconds: There are 3600 seconds in an hour.
a. Conversion Factors
To convert from miles per hour to feet per second, you will use the following factors:
\[ 1 \text{ mile} = 5280 \text{ feet} \] \[ 1 \text{ hour} = 3600 \text{ seconds} \]
b. Convert 18 mph to feet per second
To perform the conversion, you can use the formula: \[ \text{Speed in ft/s} = \text{Speed in mph} \times \frac{5280 \text{ ft}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \]
Substituting in the value: \[ \text{Speed in ft/s} = 18 \text{ mph} \times \frac{5280 \text{ ft}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \]
Calculating: \[ \text{Speed in ft/s} = 18 \times \frac{5280}{3600} \]
Calculating \( \frac{5280}{3600} \): \[ \frac{5280}{3600} = 1.46667 \]
Now, multiply to find the speed in feet per second: \[ 18 \times 1.46667 \approx 26.4 \text{ ft/s} \]
Thus, the cyclist is riding at approximately 26.4 feet per second.