Discussing the Coriolis Force & a Projectile's Missed Target

[haplo]

Hi guys, there is a problem I am having hard time interpreting, so I wonder if you can share your thoughs.
Here it is.

Homework Statement

a projectile is launched due north from a point in colatitude /theta at angle pi/4 to the horizontal and aimed at target whose distance is y (small compared to Earth radius). Show that if no allowence is made for the effects of coriolis forc, the projectile will miss it's target by a distance

x=w* ((2*y^(1/3))/g)^(1/2)*(cos(theta)-1/3sin(theta)

The Attempt at a Solution

well here is my attempt you calculate components of acceleration due to coriolis force. What confuses me, what exactly is meant by distance y. Do you treat it as vertical distance above the earth, or distance to target from launching point.
Also, how to determine the launching velocity, since it is needed for coliosis force. My initial guess is to say that velocity is zero at height y, but which height to use?

I am thinking that once components of accelerations are calculated that question is simply finding distance between two points in the plane.

So any suggestions, comments?

 

[-Vitaly-]

I think y is the distance from the origin of the projectile to the target.
I havn't done problems with Earth rotation yet. But I think I understand what they want you to find. Try this:
1st forget about the Earth rotation and treat the problem as projectile motion. It will be a parabola relative to the Earth surface (assumption:it's flat). And y would be the distance across the surface of the Earth (in common problems, it's usually x :D, but anyway). Find the velocity and the time it takes for the projectile to get from it's origin to this point y. LOOK HERE

so y=V₀^2/g, so V₀(initial velocity)=sqrt(yg) (and t=2V₀sin45^o/g total timeof the flight)

Now you need to consider that force, and find the shift (to just normal motion plane in 2D, it can be perpendicular to this plane or at an angle, depends on the force). I'm not familiar with this force, so I'm guessing it's perpendicular and F=ma, a=F/m. V_0z=0 (initial velocity in the direction of the force). x_z=at^2/2, you know the time to hit the ground from the first part.

(if the force is not perpendicular u'll get one more component of the velocity)