For this project you will need:

A 3/8 inch dowel rod, cut to your own specific measurements

One or two extension springs, your preference

Extra screws

A Phillips bit

Drill

Small door hinge

2x1 Wooden Plank cut to 18 inches

2x4 Wooden Plank cut to 18 inches (2)

3/4 inch PVC pipe

Hacksaw

Zip ties

Other miscellaneous tools (tape measurer, protractor)

(All parts and pieces can be found at Lowes or Ace Hardware)

Step 1: The Base

The base of the cannon is the most important part, and will give elevation so that the cannon is not completely touching the ground.

Take the two pieces of 2x4 wooden plank. They should be equal in size and stacked atop one another.
Using a pilot bit, drill four holes into the corner of the top plank almost through the bottom plank. If you drill too far, the screws will not take hold inside of the hole.
When the pilot holes are made, insert the four screws into four holes. Your base is now finished.

Step 2: The Barrel

Next up is the barrel. The barrel of the cannon is your 3/4 inch PVC pipe, which has a 3/8 inch dowel rod sticking out of it. Depending on how long you want your barrel and how long you want the dowel rod, the measurements will prove different.

Example:

Take the 1x2 plank and set it below the PVC pipe. It should be cut to 18 inches in this example
The PVC pipe should be as long as, or slightly shorter than the plank. Tie it to the plank with zip ties and make sure it is secure.
The dowel rod should poke a little ways out of the top of the PVC pipe (the output) and a longways out of the bottom. For this example, the top part poking out will be 2 cm and the bottom was about 10 cm. Cut the dowel rod to these measurements.

Once the barrel is attached to the plank, you may now add the necessary components to your cannon.

Take a screw, push it through a washer and then the extension spring. Install it on one side of the dowel rod. The tip of the screw should be securely in the side of the rod but not poking through to the other side. The head should still be poking out enough that you can unscrew it if needed.
Take another screw and install it at the longest end of the dowel rod, just near its end. In the picture, it would be the end that is the longest against the concrete. This screw is so you can pull back on the device and give it spring tension.
Take one more screw and install it into a washer, the other end of the spring, and then the 2x1 plank, about halfway up its length. Repeat as necessary if you are using two springs.

Step 3: The Cannon

Finally, you have come to the last part.

Take the door hinge and do precisely this;
One part of the door hinge should go on the TOP of the 2x4 wooden base.
The other part of the door hinge should go UNDERNEATH the 2x1 plank. This is the side WITHOUT the barrel.
The hinge should have come with screws for it. Install them into both parts and your cannon is finished.

Step 4: The Qwik Maths

To prove the math behind the cannon, one had to solve for time, force and initial velocity.

The math shows that with every interval of 45 deg., 50 deg., and 55 deg., the initial velocity decreased. Why is this?

As the cannon rose, the height became greater. This means there is more effort required to fire the cannon at a definite rate.
The coefficient x, the spring displacement, was kept constant, which means it is not a factor in the overall equation.
As the initial velocity, u, decreased, the force on the cannon in N (newtons) actually increased because of the increased amount of effort to keep the system constant. This is especially prevalent in this design of the cannon because of the jump in Force from 50 to 55 deg.
It can also be observed that out of the three tests, the 50 deg. angle has the most air time, because it is not too high, but not too low.