Am I taking the right approach? (Finding final velocity)

[david13579]

I've been given this problem http://i.imgur.com/7XtYt.png and I had no idea of how to come up with an answer since it is a circular path. The only thing that occurred to me is find the initial height using the chord length formula for a circle and then treat that chord as the hypotenuse of a right triangle. After finding "the height" that way I can then use an energy conservation approach to get the velocity and I get 16.78 m/s.

Is that a correct way of doing it?. Even if it is correct, not many people would remember the chord length formula so I doubt our professor intended for it to be solved that way. There has to be an easier way to do it.

 

[Delphi51]

I find "chord length" confusing.
To find the height, I drew a horizontal line from A to the vertical line.
The distance from the center of the circle to the line is 30*cos(40) = 23.
So the height at A is 30 - 23 = 7.
I get the same final answer answer you did.

 

[david13579]

I find "chord length" confusing.
To find the height, I drew a horizontal line from A to the vertical line.
The distance from the center of the circle to the line is 30*cos(40) = 23.
So the height at A is 30 - 23 = 7.
I get the same final answer answer you did.

Wow, this is more straight forward. I don't see how I see it myself.

This is what I mean by chord length . http://i.imgur.com/aNTUA.png

Thanks :)

 

[Delphi51]

Fascinating! I must attempt to derive that formula.
Funny, I never ran across it before.