Animating Curved Line

I have a tiny amount of skill with AE7;I have done a search and cannot find an answer quickly. I hope someone will give me a push in the right direction.

I want to do a stylized fireworks display....highly stylized. I want to represent the rise of a rocket. There would be several curved lines each with a circle with a stroke and no fill. The circle would rise from the center of the frame at bottom. The circles would rise....there would be a curve line tracing the ascent. The circle would bounce against the top of frame, explode or bounce down and collect in the lower corners of frame.

Soooo, I want to animate a curved line with a circle at the end. The path mimics the rise of a rocket.

There will be several "circle rockets"

Any help gratefully accepted. Thanks.