Chapter 4, Problem 19PQ

A The spiral is an example of a mathematical form appearing in nature, from the visible construction of seashells, pinecones, and galaxies to the movement behavior of certain animals. The position of a hungry animal that moves outward along a spiral path, searching for food, can be written as $\stackrel{\to }{r}\left(t\right)=A\omega t\cos \left(\omega t\right)\hat{i}+A\omega t\sin \left(\omega t\right)\hat{j}$. Write an expression for the velocity of the animal in component form.