Ferris Wheel question (Motion in 2d)

[jmedina94]

1. The Ferris wheel [...] rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s^2 .
2. Find the direction of the passenger's acceleration at this instant.
3. My attempt was using: the arctan 0.64/0.5, and that yielded ~52.0° but no dice so, could someone help me?

 

[Doc Al]

Show how you made your calculation. (Some information is missing from your problem statement.)

 

[jmedina94]

Show how you made your calculation. (Some information is missing from your problem statement.)

The problem: The Ferris wheel in the figure (Figure 1) , which rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s^2 .

The ferris wheel's radius is 14m**** Sorry about that!

Centripetal Acc = v^2/r
= 9/14 m/s^2 = 0.64

Tangential Acc = 0.5 m/s^2

Magnitude of both vectors = 0.81 m/s

θ = tan^-1 (0.64/0.5) *this was wrong*"find the direction of the passenger's acceleration at this instant"

 

[Doc Al]

The ferris wheel's radius is 14m**** Sorry about that!

Ah, good.

Centripetal Acc = v^2/r
= 9/14 m/2^2 = 0.64

Tangential Acc = 0.5 m/s^2

Magnitude of both vectors = 0.81 m/s

θ = tan^-1 (0.64/0.5) *this was wrong*

OK, but with respect to what is that angle? How do they want the direction represented?

 

[jmedina94]

OK, but with respect to what is that angle? How do they want the direction represented?

Not sure I was just testing out a method I had already practiced, probably the center of the ferris wheel?

They want it as:

θ= __° north of east

 

[Doc Al]

Not sure I was just testing out a method I had already practiced, probably the center of the ferris wheel?

The passenger is at the bottom. Draw a picture of the acceleration vector.

They want it as:

θ= __° north of east

You are on the right track, you just have to express it correctly.

 

[jmedina94]

The passenger is at the bottom. Draw a picture of the acceleration vector.

This is my rendition of the question, not sure if it's the correct way to solve the direction

 

[Doc Al]

This is my rendition of the question, not sure if it's the correct way to solve the direction

What I have in mind is this: Put a dot where the passenger is. Then draw the vectors representing the tangential and centripetal acceleration of the passenger. Then draw their sum and see where it points.

 

[haruspex]

the tangential and centripetal acceleration

Technically, I think you mean tangential and radial acceleration, though in this case, since r is constant, radial and centripetal will be the same, just opposite sign.