Convert 1100 feet per second into miles per hour: Give the final answer in the correct units number of significant- figures: Note: 1 mile = 5280 ft
The Correct Answer and Explanation is:
Answer:
1100 feet per second = 750 miles per hour
Explanation:
To convert a speed from feet per second (ft/s) to miles per hour (mph), we must convert both the distance and time units. Here’s how we do it step by step:
Step 1: Convert feet to miles
We know that 1 mile = 5280 feet.
So to convert feet to miles, divide the number of feet by 5280.1100 ft5280 ft/mile=0.20833 miles/second\frac{1100 \text{ ft}}{5280 \text{ ft/mile}} = 0.20833 \text{ miles/second}5280 ft/mile1100 ft=0.20833 miles/second
Step 2: Convert seconds to hours
There are 60 seconds in a minute and 60 minutes in an hour.
So, there are 60×60=360060 \times 60 = 360060×60=3600 seconds in an hour.
Now convert miles per second to miles per hour by multiplying by 3600:0.20833 miles/second×3600 seconds/hour=750 miles/hour0.20833 \text{ miles/second} \times 3600 \text{ seconds/hour} = 750 \text{ miles/hour}0.20833 miles/second×3600 seconds/hour=750 miles/hour
Step 3: Apply significant figures
The original value is 1100 ft/s which has 2 significant figures.
Our final answer should also be expressed with 2 significant figures to match.
Therefore, the final converted value is:750 miles per hour\boxed{750 \text{ miles per hour}}750 miles per hour
Summary
The conversion requires a clear understanding of unit relationships. By first converting the distance from feet to miles and then converting the time from seconds to hours, we ensure that our answer ends up in the desired units. Maintaining the correct number of significant figures ensures the result reflects the precision of the original data. In science and engineering, this practice is critical for clarity and accuracy.
