A projectile is fired from a cannon into the air. The initial velocity
of the projectile is known. The aerodynamic drag on the projectile is
a function of the velocity. Integrating to find a solution for this problem
could be difficult... Is there another way?

What is known:

The projectile is launched from x = 0, y = 0.

The initial velocity of the projectile is

v_{x} = 400 ft/s v_{y}
= 400 ft/s

The aerodynamic drag force is given by

Question

What is the trajectory of the projectile for

C = 0.002 ?

C = 0.004 ?

C = 0.006 ?

Approach

Because the force (and thus the acceleration)
of the particle is given in terms of the absolute value of the velocity,
integration to find position and velocity could be difficult.

Solve this problem using a method of numeric integration, such as
the finite-difference method.

Drag equation is a vector relationship that needs to be applied in
both vertical and horizontal direction.