Projection from Earth

Question

If a Particle is projected from Equator due north with a velocity $v$ and Earth is rotating with a uniform angular velocity $\omega$.

How can it be shown that the highest latitude reached will be given by the following expression? \begin{equation} \frac{\pi}{2}-(\pi-2) \frac{\omega R}{v} \end{equation}

Answer 1

No.

If v is greater than 11.2 km/s then the particle will escape. But your model predicts that for arbitrary high velocity the highest latitude will approach pi/2

Moreover as v approaches zero, this model predicts a latitude of -infinity.