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A bicycle with 19-in.-diameter wheels has its gears set so that the chain has a 6-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 190 rpm. Find the linear speed of the bicycle in in/min (correct to at least two decimal places) in/min How fast is the bike moving in mph (to two decimal places)? mph

A bicycle with 19-in.-diameter wheels has its gears set so that the chain has a 6-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 190 rpm. Find the linear speed of the bicycle in in/min (correct to at least two decimal places) in/min How fast is the bike moving in mph (to two decimal places)? mph

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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10/7,1

### Bicycle Gear and Speed Calculation Exercise A bicycle with 19-inch diameter wheels has its gears set so that the chain has a 6-inch radius on the front sprocket and a 3-inch radius on the rear sprocket. The cyclist pedals at 190 rpm (revolutions per minute). **Problem 1: Calculate the Linear Speed of the Bicycle** Find the linear speed of the bicycle in inches per minute (correct to at least two decimal places). - **Answer:** [Input Box] inches/min **Problem 2: Convert the Linear Speed to Miles Per Hour** How fast is the bike moving in miles per hour (to two decimal places)? - **Answer:** [Input Box] mph --- ### Solution Steps and Explanation 1. **Determine the Gear Ratio:** - The front sprocket radius = 6 inches - The rear sprocket radius = 3 inches - Gear Ratio = Front Sprocket Radius / Rear Sprocket Radius = 6 inches / 3 inches = 2 2. **Calculate the Rear Wheel RPM:** - Pedaling RPM (given) = 190 rpm - Rear Wheel RPM = Pedaling RPM * Gear Ratio = 190 rpm * 2 = 380 rpm 3. **Calculate the Linear Speed in inches per minute:** - The circumference of the wheel = π * Diameter = π * 19 inches - Therefore, the Linear Speed = Circumference * Rear Wheel RPM = π * 19 inches * 380 rpm 4. **Convert Linear Speed to mph:** - 1 mile = 63,360 inches - 1 hour = 60 minutes - Thus, Speed in mph = (Linear Speed in inches per minute * 60 minutes) / 63,360 inches These calculations will allow you to determine the linear speed in inches per minute and subsequently convert that speed into miles per hour. Input your answers in the respective boxes provided. *Remember to use a calculator for precise computation and rounding off to at least two decimal places.*
Transcribed Image Text:### Bicycle Gear and Speed Calculation Exercise A bicycle with 19-inch diameter wheels has its gears set so that the chain has a 6-inch radius on the front sprocket and a 3-inch radius on the rear sprocket. The cyclist pedals at 190 rpm (revolutions per minute). **Problem 1: Calculate the Linear Speed of the Bicycle** Find the linear speed of the bicycle in inches per minute (correct to at least two decimal places). - **Answer:** [Input Box] inches/min **Problem 2: Convert the Linear Speed to Miles Per Hour** How fast is the bike moving in miles per hour (to two decimal places)? - **Answer:** [Input Box] mph --- ### Solution Steps and Explanation 1. **Determine the Gear Ratio:** - The front sprocket radius = 6 inches - The rear sprocket radius = 3 inches - Gear Ratio = Front Sprocket Radius / Rear Sprocket Radius = 6 inches / 3 inches = 2 2. **Calculate the Rear Wheel RPM:** - Pedaling RPM (given) = 190 rpm - Rear Wheel RPM = Pedaling RPM * Gear Ratio = 190 rpm * 2 = 380 rpm 3. **Calculate the Linear Speed in inches per minute:** - The circumference of the wheel = π * Diameter = π * 19 inches - Therefore, the Linear Speed = Circumference * Rear Wheel RPM = π * 19 inches * 380 rpm 4. **Convert Linear Speed to mph:** - 1 mile = 63,360 inches - 1 hour = 60 minutes - Thus, Speed in mph = (Linear Speed in inches per minute * 60 minutes) / 63,360 inches These calculations will allow you to determine the linear speed in inches per minute and subsequently convert that speed into miles per hour. Input your answers in the respective boxes provided. *Remember to use a calculator for precise computation and rounding off to at least two decimal places.*
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