1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seropon [69]
3 years ago
5

A Ferris wheel has a 44-foot radius and the center of the Ferris wheel is 50 feet above the ground. The Ferris wheel rotates in

the CCW direction at a constant angular speed of 3 radians per minute. Josh boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let tt represent the number of minutes since the ride started.
Write an expression (in terms of t) to represent the number of radians Josh has swept out from the 3-o'clock position since the ride started.
   

How long does it take for Josh to complete one full revolution (rotation)?
________ minutes   

Write an expression (in terms of t) to represent Josh's height above the center of the Ferris wheel (in feet).
   

Write a function f that determine's Josh's height above the ground (in feet) in terms of t.
f(t)=

​
Mathematics
1 answer:
sleet_krkn [62]3 years ago
4 0

Answer:

Part A

The expression in terms of 't' representing the number of radians Josh has swept since the ride started is 3·t rad

Part B

The time to complete one revolution is (2·π/3) minutes

Part C.

The function 'f' that determines Josh's height above the ground (in feet) in terms of 't' is, f(t) = 44·sin(3·t + π/2) + 50

Step-by-step explanation:

The radius of the Ferris wheel = 44 foot

The height of the Ferris wheel above the ground = 50 feet

The direction of rotation of the Ferris wheel = CCW

The angular speed of the Ferris wheel, ω = 3 radians per minute

The position from which Josh boards the Ferris wheel = 3-O'Clock

The number of minutes since the ride started started = t

Part A

The expression in terms of 't' to represent the number of radians Josh has swept since the ride started = ω × t = 3 × t rad = 3·t rad

Part B

One complete revolution = 2·π radians

The time to complete one revolution = 2·π/ω = 2·π/(3 rad/minute) = (2·π/3) minutes =  0.\overline{6}·π minutes ≈ 2.0943951 minutes

Part C.

The height, 'h', of the Ferris wheel is given by the following sinusoidal relation

f(t) = A·sin(B·t + C) + D

Where;

A = The amplitude = The radius of the Ferris wheel = 44 ft.

The period, T = (2·π/3) minute

B = 2·π/T = 3

t = The time in minutes

D = The Ferris wheel's height above ground = 50 ft.

C = The horizontal shift = π/2 (Josh boards the Ferris wheel at t = 3-O'Clock which is the midline, a rotation of π/2 from the lowermost end of the Ferris wheel)

Therefore the function that determines Josh's height above the ground (in feet) in terms of 't' is presented as follows;

f(t) = 44·sin(3·t + π/2) + 50

You might be interested in
Factor 8a^2-2a^2 form of the polynomial ????
Naily [24]
8a^2-2a^2 

= 6a^2
6 0
3 years ago
Ross worked 43 hours in a certain week. He was paid $8.50 per hour and time and a half for all hours over 40. Determine his gros
kicyunya [14]
The answer  B $478.25
6 0
3 years ago
Read 2 more answers
What is the equation of this line? y=1/2x−3 y=−1/2x−3 y=−2x−3 y=2x−3 
pickupchik [31]
The answer is y=1/2x-3


3 0
2 years ago
Read 2 more answers
100 POINTS!!!!!!!!!! PLEASE HELP NEED THIS DONE AS SOON AS POSSIBLE ASAP
Llana [10]

Answer:

20.28

Step-by-step explanation:

Triangles; 4

Area of 1 Triangle; 2

Rectangles; 8

Semi Circle; 6.28

Area in total; 20.28

Hope This Helps! :)

4 0
1 year ago
Read 2 more answers
What are the common factors of 50 30 100
lesya [120]
Their common factors are :1, 2 ,5 ,10
5 0
2 years ago
Other questions:
  • The volume (in cubic meters), vv, of a rectangular room is given by the expression: v = 162-2b^6v=162?2b 6 Where bb is a positiv
    13·1 answer
  • The Suarez family travels 70 miles per hour on their family road trip
    9·1 answer
  • A shareholders' group, in lodging a protest, claimed that the mean tenure for a chief executive office (CEO) was at least eight
    15·1 answer
  • A bee flies at 20 feet per second directly to a flower bed from its hive. HThe bee stays at the flower bed for 15 minutes, then
    7·1 answer
  • 36 pennies to 72 pennies
    10·1 answer
  • Find the factors of 42 show and explain your work and list the factor pairs in a table
    15·2 answers
  • Which sentence is Correct and please take your time !!!
    7·2 answers
  • bill took a nap for 1 1/4 hour on friday and then took a nap for 3/4 hour on tuesday. how much longer was Bill's nap on friday?
    8·2 answers
  • Help me please.............
    8·1 answer
  • Windborn company has 20,000 shares of cumulative preferred 2% stock, $150 par and 50,000 shares of $25 par common stock. the fol
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!