What is the equation for finding the velocity vector of a component?

[dirk_mec1]

Homework Statement

http://img705.imageshack.us/img705/20/33060912.png

Homework Equations

http://img706.imageshack.us/img706/7514/67377660.png

The Attempt at a Solution

I don't understand how they find equation number (5). Can somebody help me with this?

 

[Päällikkö]

Please show your own work.

Use the Pythagorean theorem, sin²x + cos²x = 1, repeatedly.

 

[dirk_mec1]

Please show your own work.

I don't know how to start.

Use the Pythagorean theorem, sin²x + cos²x = 1, repeatedly.

Yes, I figured that out from (5) but the main thing is I don't know understand as to where pythagoras needs to be used.

First of all U0 is parallel to x-axis, right? (I image a x-as to the right y-axis out of the picture and z up).

 

[Päällikkö]

Well, I suppose you could do the problem geometrically, but I just crunched through the algebra.
cos²a + sin²a sin²b = cos²b + (1 - cos²a) sin²b ...
Write it out, apply the Pythagorean theorem again, regroup, Pythagorean theorem, etc.

Hope this helps?

 

[dirk_mec1]

Well, I suppose you could do the problem geometrically, but I just crunched through the algebra.
cos²a + sin²a sin²b = cos²b + (1 - cos²a) sin²b ...
Write it out, apply the Pythagorean theorem again, regroup, Pythagorean theorem, etc.

Hope this helps?

I understand the equality but its the geometry that gives the problem, I want to know where (5) comes from!

 

[dirk_mec1]

It suprises me no one was able to help with this, from what I thought was a simple geometry, problem. Anyway I figured out myself. It turns out that you'll have to give the bar a length say L and then express each the length of the sides in alpha and beta.