Convert 60 miles per hour into meters per second.
Stock of Data:
Speed is ??=60 ?miles hour
1 ?mile per hour =0.447 ?meter per second
??=60 ?miles/hour
Solution:
??=60 ?miles/hour miles
What would the key idea and sanity be?
The Correct Answer and Explanation is :
The key idea in this problem is unit conversion, specifically converting speed from miles per hour (mph) to meters per second (m/s). The goal is to ensure the calculation adheres to proper conversion factors and maintains consistent units throughout. Here’s the correct answer and explanation.
Solution:
1 mile per hour (mph) = 0.447 meters per second (m/s).
To convert 60 miles/hour60 \, \text{miles/hour} to meters/second\text{meters/second}: Speed=60 miles/hour×0.447 meters/second per mile/hour\text{Speed} = 60 \, \text{miles/hour} \times 0.447 \, \text{meters/second per mile/hour} Speed=26.82 m/s\text{Speed} = 26.82 \, \text{m/s}
Explanation (300 words):
The key to solving unit conversion problems is to start with the given value and systematically apply the appropriate conversion factors to shift between units. In this case, the goal is to convert speed from miles per hour (mph) to meters per second (m/s). The conversion factor provided states that 1 mph is equal to 0.447 m/s.
This problem illustrates a common scenario in science and engineering, where understanding the relationship between different measurement systems (imperial and metric) is critical. To perform the conversion:
- Identify the conversion factor: We know 1 mile/hour=0.447 meters/second1 \, \text{mile/hour} = 0.447 \, \text{meters/second}.
- Set up the equation: Start with the speed in miles/hour\text{miles/hour} (60 mph) and multiply by the conversion factor. This ensures the units cancel properly: 60 miles/hour×0.447 meters/second1 mile/hour60 \, \text{miles/hour} \times \frac{0.447 \, \text{meters/second}}{1 \, \text{mile/hour}} The “miles/hour” terms cancel, leaving “meters/second.”
- Perform the calculation: Multiply 60 by 0.447 to get 26.82.
By keeping track of units throughout the calculation, we can verify that the result is in the desired unit (m/s). This method not only ensures accuracy but also reinforces a systematic approach to unit conversions.
Sanity Check:
To confirm the answer, note that 1 mile is approximately 1.6 kilometers, so 60 mph is about 96 km/h. Converting this to meters per second (96÷3.696 \div 3.6) also yields approximately 26.82 m/s. This agreement ensures the result is reasonable.