Question

Nick boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.5 radians per minute and has a radius of 25 feet. The center of the Ferris wheel is 31 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating. a. Write an expression (in terms of t) to represent the varying number of radians ? Nick has swept out since the ride started. 4.5t b. How long does it take for Nick to complete one full revolution (rotation)? c. Write an expression (in terms of t) to represent Nick's height (in feet) above the center of the Ferris wheel. -31sin(4.5t) d. Write an expression (in terms of t) to represent Nick's height (in feet) above the ground. 31(1-sin(4.5t)) e. Ciara boards the Ferris wheel at the same time as Nick, but she boards at the 6 o'clock position instead. Write an expression (in terms of t) to represent Ciara's height (in feet) above the ground.

          Nick boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.5 radians per minute and has a radius of 25 feet. The center of the Ferris wheel is 31 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating.

a. Write an expression (in terms of t) to represent the varying number of radians ? Nick has swept out since the ride started.
4.5t

b. How long does it take for Nick to complete one full revolution (rotation)?

c. Write an expression (in terms of t) to represent Nick's height (in feet) above the center of the Ferris wheel.
-31sin(4.5t)

d. Write an expression (in terms of t) to represent Nick's height (in feet) above the ground.
31(1-sin(4.5t))

e. Ciara boards the Ferris wheel at the same time as Nick, but she boards at the 6 o'clock position instead. Write an expression (in terms of t) to represent Ciara's height (in feet) above the ground.

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Nick boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.5 radians per minute and has a radius of 25 feet. The center of the Ferris wheel is 31 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating.

a. Write an expression (in terms of t) to represent the varying number of radians ? Nick has swept out since the ride started.
4.5t

b. How long does it take for Nick to complete one full revolution (rotation)?

c. Write an expression (in terms of t) to represent Nick's height (in feet) above the center of the Ferris wheel.
-31sin(4.5t)

d. Write an expression (in terms of t) to represent Nick's height (in feet) above the ground.
31(1-sin(4.5t))

e. Ciara boards the Ferris wheel at the same time as Nick, but she boards at the 6 o'clock position instead. Write an expression (in terms of t) to represent Ciara's height (in feet) above the ground.

Added by Alejandra C.

Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Chapman Howard

04/21/2022

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Nick boards the Ferris wheel at the 3 o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.5 radians per minute and has a radius of 25 feet. The center of the Ferris wheel is 31 feet above the ground. Let "t" represent the number of minutes since the Ferris wheel started rotating. Write an expression (in terms of "t") to represent the varying number of radians Nick has swept out since the ride started. 4.5t How long does it take for Nick to complete one full revolution (rotation)? Write an expression (in terms of "t") to represent Nick's height (in feet) above the center of the Ferris wheel: Write an expression (in terms of "t") to represent Nick's height (in feet) above the ground: Ciara boards the Ferris wheel at the same time as Nick, but she boards at the 6 o'clock position instead. Write an expression (in terms of "t") to represent Ciara's height (in feet) above the ground.

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Transcript

00:02 Okay, so from the problem statement, we know that this ferris wheel is rotating at a constant speed of 4 .5 radiance per minute.

00:17 The radius of this ferris wheel is 25 feet.

00:25 And then if we draw this ferris wheel, you know it has some legs here, and it's saying that the center of this ferris wheel is 31 feet above the ground.

00:39 At first, we want to write an expression to represent the number of radians.

00:46 Looks like you've gotten this one right.

00:52 For a, the number of radians is 4 .5 radians per minute times t minutes.

01:07 For b, we want to know how long it takes for nick to complete one full revolution.

01:12 Well, we know that there are two pi radians in one revolution.

01:16 So it's going to be two pi radians per revolution divided by 4 .5.

01:28 Radiance per minute.

01:32 When we flip and multiply, oops, draw that line there.

01:39 When we flip and multiply this, these units radians are going to cancel and we're going to get 2 pi over 4 .5 minutes per revolution.

02:04 Okay, let's clear up some space right here for c.

02:14 We want to know in terms of t, what is nick's height above the center of the ferris wheel.

02:25 Well, the ferris wheel has a radius of 25 feet.

02:29 So we know that this is going to be 25.

02:34 The height is going to be the y coordinate around the circle.

02:37 We know that that y coordinate is modeled by the sign function.

02:43 And then we need to figure out what the period of this sign function is...

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