If an object travels 100 feet in 2 seconds, what is the object’s approximate speed in miles per hour?
(Note: 1 mile = 5280 feet)
A. 3.4
B. 3.8
C. 34
D. 38
E. 340
The Correct Answer and Explanation is:
To find the speed of an object that travels 100 feet in 2 seconds and express it in miles per hour, we can follow a systematic approach.
Step 1: Calculate the speed in feet per second
First, we determine the speed in feet per second by dividing the distance traveled by the time taken:
[
\text{Speed (feet/second)} = \frac{\text{Distance (feet)}}{\text{Time (seconds)}} = \frac{100 \text{ feet}}{2 \text{ seconds}} = 50 \text{ feet/second}
]
Step 2: Convert feet per second to miles per hour
To convert feet per second to miles per hour, we need to know the conversion factors:
- There are 5280 feet in a mile.
- There are 3600 seconds in an hour (since 1 hour = 60 minutes and 1 minute = 60 seconds).
The conversion from feet per second to miles per hour can be calculated using the following formula:
[
\text{Speed (miles/hour)} = \text{Speed (feet/second)} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{5280 \text{ feet}}
]
Substituting the values we calculated:
[
\text{Speed (miles/hour)} = 50 \text{ feet/second} \times \frac{3600}{5280}
]
Step 3: Simplifying the calculation
Now, let’s simplify this calculation:
- Calculate (\frac{3600}{5280}): [
\frac{3600}{5280} = \frac{360}{528} = \frac{15}{22} \approx 0.6818
] - Multiply by 50 feet/second: [
\text{Speed (miles/hour)} = 50 \times 0.6818 \approx 34.09
]
Conclusion
Thus, the approximate speed of the object is about 34 miles per hour.
From the provided options:
- A. 3.4
- B. 3.8
- C. 34
- D. 38
- E. 340
The correct answer is C. 34 miles per hour.