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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)=

 Mar 1, 2021

Best Answer 

 #1
avatar+31281 
+2

There are 2pi radians in a full rev

  2pi R/ 3 R/ min =   2/3 pi minutes per rev    = 2.0944 min per rev

 

Period is   2/3 pi       2pi/x = 2/3 pi     x = 3

soooo     sin 3t   

   he starts at 3 o'clock position which is 1/2 way between low and high points....so there is no phase shift

 

Amplitude = 44                 44 sin 3t    = height above center

 

Height above ground  IS shifted by 44 feet up from center         44 sin (3t) + 44  would be height above ground   ( at time = 0 he is 44 ft above ground)

 Mar 2, 2021
 #1
avatar+31281 
+2
Best Answer

There are 2pi radians in a full rev

  2pi R/ 3 R/ min =   2/3 pi minutes per rev    = 2.0944 min per rev

 

Period is   2/3 pi       2pi/x = 2/3 pi     x = 3

soooo     sin 3t   

   he starts at 3 o'clock position which is 1/2 way between low and high points....so there is no phase shift

 

Amplitude = 44                 44 sin 3t    = height above center

 

Height above ground  IS shifted by 44 feet up from center         44 sin (3t) + 44  would be height above ground   ( at time = 0 he is 44 ft above ground)

ElectricPavlov Mar 2, 2021

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