<p>No.</p>
<p>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</p>
<p>Moreover as v approaches zero, this model predicts a latitude of -infinity.</p>

CC BY-SA 4.0
2022-04-15T20:13:19.987Z
2022-04-15T20:13:19.987Z
James K
<p>If a Particle is projected from Equator due north with a velocity <span class="math-container">$v$</span> and Earth is rotating with a uniform angular velocity <span class="math-container">$\omega$</span>.</p>
<p>How can it be shown that the highest latitude reached will be given by the following expression? <span class="math-container">\begin{equation}
\frac{\pi}{2}-(\pi-2) \frac{\omega R}{v}
\end{equation}</span></p>

CC BY-SA 4.0
2022-04-15T22:31:41.890Z
Interesting formula - but where does it come from?
Roger Wood
CC BY-SA 4.0
2022-04-18T06:54:47.137Z
Why would it depend on $\omega$? From what height? $v$ is a speed, not a velocity.
ProfRob
CC BY-SA 4.0
2022-04-22T09:39:46.280Z
I’m voting to close this question because it is not about Astronomy (my be better suited to another Stack Exchange).
GrapefruitIsAwesome
<mathematics>
Projection from Earth
Particle king
# Projection from Earth

(Asked by: username_0 on 2022-04-15)

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}

**Tags:** mathematics
> **Comments:**
> **username_1**: Interesting formula - but where does it come from?  
> **username_2**: Why would it depend on $\omega$? From what height? $v$ is a speed, not a velocity.  
> **username_3**: I’m voting to close this question because it is not about Astronomy (my be better suited to another Stack Exchange).  

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## 1 answers

### Answer by username_4 on 2022-04-15. Score: 3

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.


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