Ferris Wheel: angular velocity, linear velocity, etc.

[Timcago]

A ferris wheel has a radius of 10 meters. The wheel makes one complete revolution in 20 seconds.

A) what is the angular velocity of one car on the wheel, in radians per second?
B)What is the linear velocity of the same car, in meters per second?
C)If the bottom of the wheel passes 1 meter from ground level, how high is a car if the central angle from ground level to the position of the car is 140 degrees.

My progress:

A)
--->pheta
w=--------
----->t

w=(2pi)/(20s) = (pi/10) or .3142


B)
-->Pheta*r
v=----------
---->20s

v=(2*pi*10)/(20s) = 3.14 meters per second


C)
I need help on this one. What am i supposed to do with it?

 

[galactus]

Re: Ferris Wheel

A ferris wheel has a radius of 10 meters. The wheel makes one complete revolution in 20 seconds.

A) what is the angular velocity of one car on the wheel, in radians per second?
B)What is the linear velocity of the same car, in meters per second?
C)If the bottom of the wheel passes 1 meter from ground level, how high is a car if the central angle from ground level to the position of the car is 140 degrees.

My progress:

A)
--->pheta
w=--------
----->t

w=(2pi)/(20s) = (pi/10) or .3142


B)
-->Pheta*r
v=----------
---->20s

v=(2*pi*10)/(20s) = 3.14 meters per second


C)
I need help on this one. What am i supposed to do with it?

Here's a picture. I hope I am interpreting the problem correctly.

As you can see from the diagram, the heighth y is given by

\(\displaystyle 10sin(\frac{5{\pi}}{18})\approx{7.66}\ meters\)

The heighth from the ground to the center of the wheel is 11 meters.

Adding we get 18.66 meters

 

[Timcago]

The picture did not work

Why did you multiply sin by 10 instead of 11?

Where did the 5pi/18 come from?

From the way i interpret it, i see a triangle. The legs are the distance from the ground to the center of the wheel, and from the center of the wheel to the car. The hypotenuse is the line going diagnally from the ground to the car. However i do not see how the angle going from the ground to the car coold be 140 degrees when its not the angle of the hypotenuse. What is a central angle? Is it the angle of the hypotenuse?

 

[galactus]

The central angle is the angle swept out by the car on the circle.

\(\displaystyle \frac{5{\pi}}{18}\) is 50 degrees in radians.

I don't know why the picture won't work. It's fine in the preview.
Try right clicking on the little red x and clicking on 'show picture'. It comes up when I do that.

Can you post a picture of the wheel?. I am just interpreting the problem best I can with no picture.

Suppose the car is one foot above the ground, directly 10 feet under the radius point. The car then starts going upward, counterclockwise, until it sweeps out 140 degrees of the circle. I have 90 and 50 marked on the picture, that's 140. I just used 1 foot above the ground plus the 10 foot radius plus y of the triangle I have drawn which has a 50 degree angle.

EDIT: The picture works now, I hope.

 

[Timcago]

There is no picture. Yours looks correct to me