Calculus based physics: Projectile motion

Say I have a ball that which describe the path of a parabola which equation is $\large (x-2)^2=\frac{-4}{5}(y-5)$

Say I want to find the velocity at its highest point, the vertex.
So I find the derivative of this equation, which is $\large y'(x)=\frac{-5}{2}(x-2)$

Its highest point is 2, thus I get velocity = 0m/s

Question

Calculus based physics: Projectile motion

Say I have a ball that which describe the path of a parabola which equation is $\large (x-2)^2=\frac{-4}{5}(y-5)$

Say I want to find the velocity at its highest point, the vertex.
So I find the derivative of this equation, which is $\large y'(x)=\frac{-5}{2}(x-2)$

Its highest point is 2, thus I get velocity = 0m/s

zepp · Answer

Now the problem is, I know that I got 0m/s because the slope at the vertex is 0, but also because the speed in the y-direction is 0m/s, BUT x-direction is not, so how do I find the speed in the x-direction at the vertex using calculus?

(I know that the speed in the x-direction is constant everywhere on the parabola, but how to find it exactly on the vertex? Without using the 4 equations of kinematics, only calculus?)

zepp · Answer

@ash2326 Can you help me please?