Displacement caused by Coriolis effect -

[James1991]

http://img121.imageshack.us/img121/6590/mwsnap001.jpg

The image above shows the question I'm stuck on.

I've done the first part and got the force per unit mass to be -2wV'cos$$\lambda$$

But I have no idea how to get the equation for the eastward displacement due to the Coreolis.

Any help would be appreciated
Thanks :)

 

[kuruman]

What are the three x,y,z equations of motion for this case?

 

[James1991]

I was using an equation of motion which relates the acceleration in the Earth's rotating frame and a non moving frame and i tried to intergrate it to get the answer they wanted

a = a' - 2wXv' + wX(wXx')

where a, a', w, v' and x' are vectors and X is the cross product

 

[kuruman]

There are three equations of motion, not just one, because there are three independent directions in space. Assume that z is "up", x is due East and and y is due North from the latitude of the object. What the three equations of motion?

 

[James1991]

There are three equations of motion, not just one, because there are three independent directions in space. Assume that z is "up", x is due East and and y is due North from the latitude of the object. What the three equations of motion?

z = 1/2gt^2

x = v^2sin2(theta)/g

pretty sure we don't need y in this case. am i along the right lines? still not sure how to get what they got using these

 

[kuruman]

Look for differential equations. What is the general form for the acceleration in the rotating frame? What happens when you write it in component form? Yes, you will not need y in this case, but it wouldn't hurt to write all three of them and then use what you need.