Conservation of Energy in a Cart Falling from a Table

[GreenPrint]

Homework Statement

delta E = 0 = delta K + delta U
delta U = -delta K
mg(h - h_0) = m/2 (v_0^2 - v^2)

or in its common form

mgh - mgh_0 = (m v_0^2)/2 -(m v^2)/2
mgh + (m v^2)/2 = (m v_0^2)/2 + mgh_0

which is how msot people perfer to memorize very simple intro to physics conservation of energy equations but I prefer this formula as it is more sipmle

mg(h - h_0) = m/2 (v_0^2 - v^2)

now my question is velocity conserved in the following situation

a cart is riding on a horizontal surface I know the velocity right before it leavs the horizontal surface and fall to the floor

now this velocity is a horizontal velocity right so let's let this equal the velocity naught ok but the thing is that the final velocity will be equal to the velocity naught, except not really becasue of drag force but that's not a topic of AP physics B, so the horizontal velocity is the only velocity that changes but in this case there would be a final velocity but the velocity naught in the y direction would be zero because it only has a initial horizontal velocity...

Like I'm trying to solve this problem and can't becasue I think in order to do so I have to use both a horizontal velocity for the inital right before the cart which is perfectly fine but then I have to solve for the final vertical velocity in order to solve for the kinetic energy right before it reachs the ground which I don't like one bit

how can i mix and match horizontal velocities and vertical velocities whenever I want...

Heres the problem

[PLAIN]http://img338.imageshack.us/img338/9841/physics1.jpg

heres the scoring guidelines for (d) which I need help with
[PLAIN]http://img401.imageshack.us/img401/6328/physics2.jpg

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Like I'm trying to solve this problem and can't becasue I think in order to do so I have to use both a horizontal velocity for the inital right before the cart which is perfectly fine but then I have to solve for the final vertical velocity in order to solve for the kinetic energy right before it reachs the ground which I don't like one bit

how can i mix and match horizontal velocities and vertical velocities whenever I want...

Once you've calculated the speed of the cart as it leaves the table, all you need (for part d) is conservation of energy. You don't need to solve for the final vertical velocity, although it's perfectly fine if you do (just more work). In projectile motion, treat horizontal and vertical motion separately, since only the vertical is accelerated.