Mechanics Projectile / Coriolis Effect

[Ted123]

Homework Statement

[PLAIN]http://img232.imageshack.us/img232/82/mechanics.jpg

Homework Equations

The Attempt at a Solution

Where to start?

 

[tiny-tim]

Welcome to PF!

Hi Ted123! Welcome to PF!

Start with the definition of Coriolis force …

2m u x Ω ​

 

[Ted123]

Hi Ted123! Welcome to PF!

Start with the definition of Coriolis force …

2m u x Ω ​

Can you elaborate on this as I'm not at all sure where the method's taking me - I haven't seen that definition before!

 

[tiny-tim]

Can you elaborate on this as I'm not at all sure where the method's taking me - I haven't seen that definition before!

What definition of Coriolis force have you been using?

(and btw, what approximate formula will you be using for the time of flight?)

 

[Ted123]

What definition of Coriolis force have you been using?

(and btw, what approximate formula will you be using for the time of flight?)

Actually, I tell a lie: I've seen it like

${\bf {text F}_{coriolis} = -2m(\omega \times {\bf u} )$

I've also seen the formula:

$D' {\bf x} = D {\bf x} + \omega \times {\bf x}$

$mD^2{\bf x} = m{\bf g}$

and $\displaystyle{\bf x}(t) = {\bf x}(0) + {\bf u}t + \frac{1}{2} {\bf g}t^2 + {\bf u} \times \omega t^2 + \frac{1}{3}{\bf g} \times \omega t^3$

 

[tiny-tim]

Hi Ted123!

Well, the last formula looks correct, but you'll never remember it for the exam! …

so can you prove it (from 2m u x ω)?