Coupled motions

1. Feb 3, 2014

Jonsson

Hello there,

A weather ballon is released, and its acceleration in the z-x-plane, a is governed by a buoyancy force, B, which is constant in the k-direction. gravitational acceleration, 9.81 m/s^2, in the k-direction, and FD, which is is like this:

$$F_D = -D|\vec{v}|\vec{v}$$

where D is some constant. Furthermore, the balloon is experiencing some wind in the i-direction:

$$\vec{w} = w\vec{i}$$

Then:

1. Does the following look reasonable:

$$F_D = D(|\vec{w}|\vec{w} - |\vec{v}|\vec{v})$$

And if the above is correct, 2., I fail to see how this can be a coupled motion:

$$\vec{a} = {D \over m}(|\vec{w}|\,\vec{w} - |\vec{v}|\,\vec{v}) + ({F_B \over m} - g)\vec{k}$$

Will you kindly explain how it is coupled?