The term ballistics refers to the motion of an object that is launched off the surface of the Earth (or of any planet) and is pulled back down by gravity. If you throw a baseball into the air, it follows a ballistic path. A missile that is launched from one point on the Earth and comes down on another point follows one also (hence the term ballistic missile).
To study ballistic motion, you can break it down into two basic parts: vertical motion and horizontal motion. Vertical motion is a projectile’s upward and downward movements. To observe just this part of ballistics, simply throw a ball straight up into the air. As soon as it leaves your hand it will begin to lose speed at a constant rate until it reaches the point along its path where it has no speed at all. Here its motion will be reversed and it will begin to fall back down, picking up speed at the same rate that it lost speed going up. Due to uniform acceleration, this rate will always be 9.8 meters per second squared near the surface of the Earth.
You can look at this upward and downward motion as positive and negative acceleration. When the ball is heading upward gravity is pulling on it in the exact opposite direction. This pull imparts a negative acceleration on the ball which explains why it loses speed. Once gravity has drained the ball of all its upward momentum, the ball is free to start moving with gravity’s pull instead of against it. As it comes back down to Earth it undergoes the exact same positive acceleration we learned about in free fall on Page 5.
It is important to note that the upward motion of the ball and its downward motion are perfectly symmetrical. In other words, a ball’s motion path upward, including its speed at every point along that path, is an exact copy of its motion path downward. The only difference is that the two paths travel in opposite directions. To illustrate this point lets say that you throw a ball straight up with an initial speed of 20 kilometers per hour. When the ball has reached the midway point in its upward path, the point which is an equal distance between its starting point and its maximum height, it will be traveling at ten kilometers per hour. It continues to lose speed and finally turns around. When the ball passes this midway point again on its return trip down to Earth it will again be traveling at ten kilometers per hour only this time in the opposite direction. And when it comes back down to the height from which it started (the height at which it left your hand) it will have regained its initial speed of 20 kilometers per hour.
Another useful way to look at the vertical motion component of a ballistic path is through the balance of kinetic and potential energy. An object’s kinetic energy is its energy of motion, its momentum, while potential energy is just that, potential. For example, at the moment when a ball is launched into the air it has 100% kinetic energy and 0% potential energy. However, as the ball loses speed its kinetic energy drops and its potential energy rises. At the moment when the ball is at its maximum height it has 0% kinetic energy and 100% potential energy. And as the ball begins its return trip, the process is reversed. The important thing to keep in mind, however, is that the ball’s total energy always stays the same. The amount of potential and kinetic energy it has anywhere along its path always adds up to the same number.
Now let’s add the second part of ballistic motion, namely horizontal motion or ground speed. This is the forward motion of a projectile. While the vertical speed of an object on a ballistic path is always changing, its horizontal speed stays constant. Its horizontal energy is always 100% kinetic.
So, what does horizontal motion do to an object’s ballistic path? When a projectile has only vertical motion it travels on a straight line up and down but if horizontal motion is added this line stretches out into a symmetrical arc. The shape of this arc depends only on the angle that the projectile is launched at. If it is launched at a low angle the arc will be very shallow and if it is launched at a high angle the arc will be very steep.
Launching angles also determine the distance over the ground a projectile will travel. You should know from experience that if you throw a ball at nearly a 90 degree angle (straight up) it won’t travel very far. It simply doesn’t have enough forward momentum. In fact, if you throw it exactly at 90 degrees it should come right back to you. Likewise, if you throw a ball at a low angle, like ten degrees, it still does not travel very far across the ground. Gravity pulls it down too quickly. In order for a projectile to achieve its maximum distance it must be launched at a 45 degree angle which is half way between straight forward and straight up. This midway angle seems to strike the perfect balance between horizontal and vertical speed.
To see a simulation of vertical ballistic motion click here or to see a full ballistic simulation click here (both require a Java enabled browser).
