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Week Six – Application Assignment
Answer the following questions in a Word document and upload the document to the
appropriate drop box.
1) The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the
figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist pedals at a rate of 1
revolution per second.
a) Find the speed of the bicycle in feet per second and miles per hour.
- pedal sprocket: 2𝜋𝑟 = 2𝜋(4′′ ) = 8𝜋
- wheel sprocket: 2𝜋𝑟 = 2𝜋(2′′ ) = 4𝜋
𝑝𝑒𝑑𝑎𝑙 𝑠𝑝𝑟𝑜𝑐𝑘𝑒𝑡 8𝜋
𝑤ℎ𝑒𝑒𝑙 𝑠𝑝𝑟𝑜𝑐𝑘𝑒𝑡 4𝜋
2 wheel turns for each pedal sprocket turn.
- speed of bicycle: 2𝜋(14” ∗ 2) = 56𝜋 "⁄𝑠
- speed of the bicycle in feet per second:
- speed of the bicycle in miles per hours:
= 𝟏𝟒. 𝟔𝟕 𝒇𝒕⁄𝒔
= 𝟗. 𝟗𝟗𝟔𝒎𝒊𝒍𝒆𝒔/𝒉
b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist
travels in terms of the number n of revolutions of the pedal sprocket.
- Distance travel d = (revolutions of front sprocket)*(distance travelled per revolution)
- distance travelled per revolution:
= 0.0027766 𝑚𝑖𝑙𝑒𝑠⁄𝑟𝑒𝑣
- revolutions of front sprocket: n
𝒅(𝒏) = 𝒏(𝟎. 𝟎𝟎𝟐𝟕𝟕𝟔𝟔 𝒎𝒊𝒍𝒆𝒔⁄𝒓𝒆𝒗)
c) Write a function for the distance d (in miles) a ...
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