Return to my Cinderella pages
Return to my Mathematics pages
Go to my home page
© Copyright 2003, Jim Loy
Here is the trajectory (path) of a cannon ball. This trajectory is a parabola, and is called a ballistic trajectory. You can adjust the angle of the cannon by moving the diagonal line. I have not allowed you to change the amount of gun powder. You will see that the maximum possible range is about 45 degrees. Simple physics shows that this angle is exactly 45 degrees. If we want the maximum altitude, we shoot straight up in the air (90 degrees). Air resistance does not affect the trajectory very much, especially not enough to be seen on this small scale. The trajectory is almost completely determined by the initial velocity and gravity.
Question: This simulation uses the simplifying assumption that the Earth is flat. What is the shape of the above trajectory if we take into account the fact that the Earth is round? See the answer, below.
Answer: The actual trajectory is a long narrow ellipse, with the Earth's center at one of the two foci. The cannon ball is actually in orbit, but the surface of the Earth gets in the way. The difference between this ellipse and the above parabola is so small as to be almost unmeasurable. And so the above parabola, with its simpler equations, is good enough.
The above Java interactive demonstration was created with Cinderella (a geometry program).
Return to my Cinderella pages
Return to my Mathematics pages
Go to my home page