Look out! I'm still working on this!

This is the trajectory of your last shot. You will probably want to refer to it while looking at the plots below, as they are made from the data from this shot. It might even be a good idea to open another Mosaic (or netscape, etc.) window so you can look at it and the plots at the same time...

First, its probably a good idea to explain what you are seeing in the picture above. It is a graph showing the horizontal and vertical positions of the projectile as it travels through the air. The dots you see are drawn every tenth of a second, with the bigger dots appearing each second. You can imagine that the projectile is traveling from left to right, starting at the end of the cannon, traveling up, then hopefully descending somewhere near the cow. It would be moving faster when the dots are far apart, slower when they are close together... This picture is like what you would see from a real projectile if it were allowed to leave small puffs of smoke in the air behind it ten times per second.

Something you may notice here is that the trajectory doesn't look exactly like a parabola. This is because you told the simulator to shoot the particle in air. When something is travelling through the air, not only is gravity acting on it, but so is friction. Friction "eats away" at the projectile's total energy as time goes on, which is why the trajectory looks a bit warped. In this case the force of friction is proportional to the velocity and is always pointing in the opposite direction of the motion. (i.e. when it goes faster, the force is bigger -- you can verify this by riding a bike -- On a windless day, if you ride really slow you'll notice the air hardly pushes against you, but if you ride really fast, the air pushes against you more, making it difficult to keep up your speed. -- You should also notice that no matter what direction you are travelling, the air is always pushing against you. )

This is a plot of the projectile's vertical position as a function of time. If you look closely you can see that the curve has a different shape before it reaches the maximum than it has afterwards. Remember that the force due to air friction is opposite to the direction of motion. That means the vertical component is pointing down when the projectile travels up, and points up when the projectile is traveling down, like in the picture below.

One effect of this is that the projectile gets pulled down harder before it reaches its maximum height. Another, probably more interesting effect occurs after the projectile reaches its maximum. After this point, the vertical component of the friction force is pointing in the opposite direction of gravity. As the projectile drops from its maximum height, gravity makes it fall faster, which in turn makes the frictional force increase until it can even equal the force of gravity. After that point, the two forces start to balance each other, (the projectile approaches equilibrium) until the projectile is not accelerating in the vertical direction anymore. That means there is a maximum velocity an object can reach when it is falling in air. This velocity is affectionately known as its terminal velocity. (In the case of this projectile, the terminal velocity is 98 meters/second.) Once the projectile reaches this velocity, it can never go any faster unless some external force makes it do so.

These are graphs of the projectile's velocity and acceleration due to the frictional force as it changes in time from the shot you just made. There are three lines on each: the red one is the horizontal component, green one is the vertical component, and the blue one is the total magnitude. Notice that the shapes of the two plots are exactly the same, just one is bigger than the other. This is because the frictional force is proportional to the velocity. This means the frictional force is just the velocity times a constant number.

There are a few things you should probably notice about these plots. First, look at the green curve, or vertical component of the force and velocity. Notice that it starts out positive then crosses zero and ends up negative. This means that it starts out traveling upwards and ends up traveling downwards. Also notice that the point where this switch takes place occurs exactly at the same time as the projectile reaches its maximum height. You should look at how this curve relates to the vertical position curve above. Hopefully you can see that the shape of the velocity (and also friction force) curve depends on the slope of the position curve. When the slope of the position curve is positive, so is the velocity. When it is zero, so is the velocity. And, when the slope is negative, so is the velocity. Try to see if you can see the same relationship between the red curve (which is the horizontal component of the velocity) and the horizontal position curve below.

Now look at the blue curve. This is the total magnitude of the force and velocity. Notice that it isn't just the sum of the vertical and horizontal components. That is because both the force and velocity are vector quantities and must be added as vectors. Also, depending on the characteristics of this particular shot, you might be able to see a few other things:

Here is a graph of the horizontal position as it changes in time. If there were no friction, it would be a straight line. However, since the projectile is flying through air, friction causes the curve to droop over, with the projectile making less and less progress during each moment in time.

Finally, here is a plot of the projectile's energy as a function of time. The green curve is the projectile's potential energy, which is proportional to how high it goes in the air. Notice that it starts and ends at zero, since the projectile starts and ends on the ground, and peaks when the projectile is at its highest point. The red curve is its kinetic energy, which is related to how fast the projectile goes. It decreases consistently as friction reduces the projectile's velocity. The blue curve is the projectile's total energy which is just the sum of the kinetic and potential energies. Energy, unlike velocity and force is just a regular number (not a vector) so its legal to add them arithmetically. Notice that it is always decreasing. This is the work of the frictional force. This is because it is a nonconservative force. In other words, it changes the total energy of the projectile. Gravity, on the other hand, is a conservative force. The total energy is not changed when it acts on the projectile. The best way to see this is to try shooting the projectile with the "shoot in a vacuum" option turned on, so that friction doesn't obscure things.