Q:

How does an object's motion behave if dropped from an aeroplane travelling diagonally upwards?

Imagine an aeroplane travelling with velocity $v$ at some angle $\alpha$ from East to North. 
A box is dropped from the aeroplane.
What would the projectile of the box be? Would it be a parabola with an initial y-component of velocity acting upwards, or would it travel as a downward curve (with an initial y-component of velocity acting downwards)?
My reasons for thinking both:
Parabolic projection
My explanation for this would be that the box will have the same initial components of velocity as the aeroplane at the time it is dropped. Since the aeroplane has a y-component of velocity acting upwards and an x-component of velocity it would travel in a parabola, as in conventional projectile motion. 
Downward curve
(By "downward curve" I mean a curve with negative gradient increasing in magnitude.) My explanation for this would be that as soon at it is let go the only force acting on the box would be its weight, and hence it couldn't travel upwards. As well as this, when I visualise in my head a box being dropped from an aeroplane, I can't imagine it's possible to travel in a diagonally upward direction once it's been let go.
Can someone explain to me which type of motion it has and why? 

A:

It will travel along a parabola (ignoring drag from the air here), initially with upward velocity, as you describe in your first scenario.
You're correct that the only force acting on the box is its weight, but this means it will have downward acceleration immediately, not necessarily downward velocity. Eventually the downward acceleration will lead to negative velocity, but initially the box travels with the same velocity as the plane.
Travelling upward once it's been let go isn't strange at all. If you throw a ball into the air, it travels upward for a while before beginning to drop, and this isn't strange...

A:

Your question has great practical significance: it is the very essense of loft bombing/LABS.
Since nuclear weapons can damage/destroy an attacking plane, it was deemed necessary to devise a method to release the bomb and to increase the separation between the air burst and the aircraft.
I recommend watching this training video: http://www.youtube.com/watch?v=3dIqfN_aPtY

