(I am certainly not known for my art)
I had the flower and cannon meet using the rule of thirds. The goal was to try and draw attention to the cannon and away from the stairs.
Further, the cannon doesn't move until the flower finishes saying hello to keep the viewer focused on the flower.
As the cannon sneezes, the body of the cannon squashes down before releasing one last sneeze!
The cannon ball follows an arc on its initial release.
I used Pose to Pose on the cannon ball. I went back to add a very subtle bounce after the initial hit (cannon balls are heavy), but found this was easiest after having its landing point marked.
I used straight ahead with the cannon animation.
Though this animation went alright, there were a few things I had trouble with:
Sources
Sneeze Sound: http://soundbible.com/526-Sneeze.html
Sniff Sound: http://soundbible.com/958-Sniff-Short.html
Hello Sound: http://soundbible.com/769-Hello.html
Bigger Sneeze: http://soundbible.com/202-Achoo-Sneeze-Sound.html
Cannon & Flower: TurboSquid