Projectile problem - mathematical treatment

To introduce you to Maple, we'll use it to analyze the problem of projectile motion in two dimensions. However, before we can tell Maple what to do, it is essential that we understand the problem.

Suppose our projectile is fired at time t=0 from the initial position . The initial speed is and the projectile is fired at an angle with the horizontal. If air resistance is ignored, Newton's second law can be used to derive the following equations for the position (x(t),y(t)) of the projectile at time t. The letter g is used to stand for the acceleration due to gravity.

In these equations, t is the independent variable, x and y are the dependent variables, and g, , , , and are parameters. That is, we think of g, , , , and as being constants. Once we have set values for the constants, then the equations give us the x and y coordinates of the projectile as functions of t.

Here are some examples of the kinds of questions that these equations can be used to answer.

1. If the projectile is fired at time t=0, what is the time when it hits the ground?
2. How far away from where it is fired does the projectile hit the ground?
3. What angle gives the maximum distance?