Thank you for visiting A school track athlete sprints 100 yards in 15 seconds a Determine the number of feet per second the runner is traveling at Show your. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure, let's break down the solution step by step:
### (a) Determining the Speed in Feet per Second
1. Convert Yards to Feet:
- We know that 1 yard = 3 feet.
- The athlete sprints 100 yards.
- So, the distance in feet is:
[tex]\[
100 \text{ yards} \times 3 \text{ feet/yard} = 300 \text{ feet}
\][/tex]
2. Calculate Feet per Second:
- The athlete covers 300 feet in 15 seconds.
- To find the speed in feet per second, we divide the distance by the time:
[tex]\[
\frac{300 \text{ feet}}{15 \text{ seconds}} = 20 \text{ feet/second}
\][/tex]
The athlete is traveling at 20 feet per second.
### (b) Determining the Speed in Miles per Hour
1. Convert Feet per Second to Miles per Hour:
- We know there are 5280 feet in a mile.
- There are 3600 seconds in an hour.
- To convert the speed from feet per second to miles per hour, we can use the formula:
[tex]\[
\text{Speed in miles per hour} = \frac{\text{Speed in feet per second} \times 3600 \text{ seconds/hour}}{5280 \text{ feet/mile}}
\][/tex]
- Substitute the values we have:
[tex]\[
\text{Speed in miles per hour} = \frac{20 \text{ feet/second} \times 3600 \text{ seconds/hour}}{5280 \text{ feet/mile}} \approx 13.6 \text{ miles/hour}
\][/tex]
After rounding to the nearest tenth, the runner's speed is 13.6 miles per hour.
So, the detailed solution is:
- The athlete's speed is 20 feet per second.
- The athlete's speed in miles per hour is approximately 13.6 miles per hour after rounding to the nearest tenth.
### (a) Determining the Speed in Feet per Second
1. Convert Yards to Feet:
- We know that 1 yard = 3 feet.
- The athlete sprints 100 yards.
- So, the distance in feet is:
[tex]\[
100 \text{ yards} \times 3 \text{ feet/yard} = 300 \text{ feet}
\][/tex]
2. Calculate Feet per Second:
- The athlete covers 300 feet in 15 seconds.
- To find the speed in feet per second, we divide the distance by the time:
[tex]\[
\frac{300 \text{ feet}}{15 \text{ seconds}} = 20 \text{ feet/second}
\][/tex]
The athlete is traveling at 20 feet per second.
### (b) Determining the Speed in Miles per Hour
1. Convert Feet per Second to Miles per Hour:
- We know there are 5280 feet in a mile.
- There are 3600 seconds in an hour.
- To convert the speed from feet per second to miles per hour, we can use the formula:
[tex]\[
\text{Speed in miles per hour} = \frac{\text{Speed in feet per second} \times 3600 \text{ seconds/hour}}{5280 \text{ feet/mile}}
\][/tex]
- Substitute the values we have:
[tex]\[
\text{Speed in miles per hour} = \frac{20 \text{ feet/second} \times 3600 \text{ seconds/hour}}{5280 \text{ feet/mile}} \approx 13.6 \text{ miles/hour}
\][/tex]
After rounding to the nearest tenth, the runner's speed is 13.6 miles per hour.
So, the detailed solution is:
- The athlete's speed is 20 feet per second.
- The athlete's speed in miles per hour is approximately 13.6 miles per hour after rounding to the nearest tenth.
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Rewritten by : Jeany
