Finding the velocity of flow described by a vector field

[Snoldermus]

Homework Statement

Consider the surface, S, in the xyz-space with the parametric representation: S: (, ) = [cos() , sin() , ] −1/2 ≤ ≤ 1/2 0 ≤ ≤ os().
The surface is placed in a fluid with the velocity potential f of a flow: = y*^2 + z*^2
a) Find the velocity of the flow described by a vector field (, , ).

b) What is the velocity at the point = (−1,5,0)

Homework Equations

The Attempt at a Solution

so this is the solution given for a and b, however i don't understand the answer at b. How can the different equations just be summed into one number, i would understand it if was squared--> then taken the sum of the numbers --> then taken the squareroot. Can anyone confirmed that this solution is wrong?[/B]

 

[scottdave]

parametric representation: S: (, ) = [cos() , sin() , ] −1/2 ≤ ≤ 1/2 0 ≤ ≤ os().

Please clarify the surface S(,) and missing arguments for cosine, sine and the z coordinate.

 

[Snoldermus]

Sry, i copied it and it messed it up a bit, thought i fixed it though here is a picture should be clear

 

[Delta2]

Velocity is a vector, so just saying that velocity is 16 seems to be wrong.

Also the magnitude of the velocity vector at that point is not 16.

 

[Snoldermus]

Thanks :) what i thought aswell