Mathematics
MA141 Grantham University Week 6 Mathematics: Application Assignment

### Question Description

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.

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.

c) Write a function for the distance d (in miles) a cyclist travels in terms of the time t (in seconds). Compare this function with the function from part (b).

2) A car’s rear windshield wiper rotates 125°. The total length of the wiper mechanism is 20 inches and the length of the wiper blade is 12 inches.
Find the area wiped by the wiper blade

3) A six-foot person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When the person is 132 feet from the tower and 3 feet from the tip of the shadow, the person’s shadow starts to appear beyond the tower’s shadow.

a) Draw a right triangle that gives a visual representation of the problem.
Label the known quantities of the triangle and use a variable to
represent the height of the tower.

b) Use a trigonometric function to write an equation involving the unknown quantity.

c) What is the height of the tower?

4) An airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer. Let θ be the angle of elevation from the observer to the plane. Find the distance d from the observer to the plane when:

a) θ = 30°

b) θ = 90°,

c) θ = 120°

5) A baseball is hit at an angle horizontal with the ground. Suppose the initial velocity is 100 feet per second. An outfielder catches the ball 300 feet from home plate. Find the angle given the range is determined by the following function

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
=
=2
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:

56𝜋"⁄𝑠

- speed of the bicycle in miles per hours:

12
(

= 𝟏𝟒. 𝟔𝟕 𝒇𝒕⁄𝒔

14𝜋
𝑓𝑡⁄𝑠)(3600𝑠⁄ℎ)
3

5280𝑓𝑡⁄𝑚𝑖𝑙𝑒

= 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:

14𝜋
𝑓𝑡)
3

(

5280𝑓𝑡/𝑚𝑖𝑙𝑒𝑠

= 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 ...

jesusale932 (2943)
Boston College
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