- Express the speed as a fraction: \(\frac{40 \text{ miles}}{1 \text{ hour}}\).
- Use conversion factors to change miles to feet (\(\times 5,280\)) and hours to seconds (\(\div 3,600\)).
- Perform the calculation: \(\frac{40 \times 5,280}{3,600} \approx 58.67\).
- Round to the nearest whole number to get the final answer: \(\boxed{59 \text{ feet per second}}\).
Explanation
- Problem Analysis and Conversion Factors
To convert a speed from miles per hour to feet per second, we must perform dimensional analysis using the given conversion factors. We know that the jackrabbit's speed is \(40\) miles per hour. We need to convert miles to feet and hours to seconds. We are given the conversion \(1 \text{ mile} = 5,280 \text{ feet}\). Additionally, we know that \(1 \text{ hour} = 60 \text{ minutes}\) and \(1 \text{ minute} = 60 \text{ seconds}\), which gives \(1 \text{ hour} = 3,600 \text{ seconds}\).
- Calculating the Speed in Feet per Second
To find the speed in feet per second, we express the speed as a fraction and multiply by the appropriate conversion ratios:
\[ \text{Speed} = \frac{40 \text{ miles}}{1 \text{ hour}} \times \frac{5,280 \text{ feet}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3,600 \text{ seconds}} \]
By canceling out the units (miles and hours), we are left with feet per second:
\[ \text{Speed} = \frac{40 \times 5,280}{3,600} \text{ feet per second} \]
Calculating the numerator: \(40 \times 5,280 = 211,200\).
Now, divide by the number of seconds in an hour:
\[ \frac{211,200}{3,600} \approx 58.67 \text{ feet per second} \]
- Rounding and Final Conclusion
Rounding the result of \(58.67\) to the nearest whole number gives \(59\). Comparing this to the given options, we find that \(59 \text{ feet per second}\) corresponds to option (b). Therefore, the jackrabbit's speed is \(\boxed{59}\) feet per second.
Examples
Converting units of measurement is a fundamental skill in science and engineering. For example, meteorologists often convert wind speeds from knots to miles per hour or kilometers per hour to better understand local weather patterns. Similarly, athletes may convert their running speeds between different units to compare their performance with international records. Mastery of these conversions ensures accurate communication and understanding of physical data in everyday life.