Math Help - Implicit differentiation

1. Implicit differentiation

Hi, just wondering if I got this one right.

A circle is given by an equation (see image). The first task is to find y' and y'' in the point (0,0). This I have done. Using implicit differentiation I got:

y'=2 and y''=-5

"The circle describes the path of a particle. In the point (0,0) its speed in the x-direction, dx/dt, is 2 m/s. Find the particle's speed in the y-direction and the total speed."

My reasoning goes like this:

Since y' in the point (0,0) is 2, the particle's speed in the y-direction is double that in the x-direction. Therefore it must be 4 m/s.

The total speed (v) is the sum of the two vectors x and y, and can be found using Pythagoras:

v^2=2^2+1^2

v=√5

Does this make sense to you, or am I way off?

Thanks

2. I agree with everything up until this point:

v^2=2^2+1^2.

I think you meant to write

v^2=4^2+2^2, right?

3. Originally Posted by Ackbeet
I agree with everything up until this point:

v^2=2^2+1^2.

I think you meant to write

v^2=4^2+2^2, right?
Yes, that's what I meant. Glad to see my logic was right. I had been mulling over this problem for a while now..

4. Ok, I think you're good to go on that one. Have a good one!