Question

a cyclist is riding 18 mph
a. What conversion factors should be used to convert 18 mph to feet per second?

B. how many feet per second is the cyclist riding?

Answer 1

To convert miles per hour (mph) to feet per second (ft/s), we can use the following conversion factors:

1. **Miles to feet**: There are 5280 feet in a mile.
2. **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**.