Coriolois Force Acting on Carousel

You are on a carousel with a linear speed $\displaystyle \vec{v}$, such that $\displaystyle \frac{d}{dt}\vec{v}=\vec{b}+.5\vec{v}$

and, $\displaystyle \vec{b}\cdot\vec{v}=0$

Let $\displaystyle \vec{C_t}(t)$ denote the tangential component of the Coriolis force exerted on your body at time t and let its magnitude equate 1. Calculate

$\displaystyle \frac{d}{dt}|\vec{C_t}|^2(t) $

The normal component of angular velocity is constant.

I have been working on this problem for >6 hours to no avail. I have tried to get a detailed explanation as to how to do this, but no luck. There are only 4 sample questions in the textbook dealing with the Coriolis effect, which I can get non of.

Help?

I know that the velocity vector is tangent to the circle of rotation, and that the angular velocity is perpendicular to the plane of rotation, as well the force is directed away from the carousel, in the same plane as the velocity.

Re: Coriolois Force Acting on Carousel

We could solve this DE.

Having dot product with v we get

$\displaystyle \vec{v}\frac{d}{dt}\vec{v}=\vec{v}\vec{b}+.5\vec{v }\vec{v}$

and now we have

$\displaystyle \frac{d}{dt}(\vec{v} \: ^2)=\vec{v} \: ^2$.