# Homework #1: ODE's & Particle Dynamics

### Due on Tuesday, Sept. 18, 2007

**(10pt) Problem A: Ballistic Motion**

Given a location of a gun at (0,0,0), write an 3D artillery simulator that
can take in the mass of the projectile, amount of powder,
the azimuth and elevation of the gun barrel. Use the amount of powder and
the mass of the projectile to determine the muzzle velocity. Account for
gravity and air friction. Assume that one kilogram of powder produces 10,000
newtons of force. Assume instantaneous acceleration as a result of the powder
going off. Air friction coefficient is constant. Set it to be
50 kg/s initially. The gun and target are both on the X-Z plane.

**(15pt) Problem B: Spring-Mass Simulator**

A spring hands vertically in its equilibrium or resting position. Given a
user-defined mass *m* attached to the spring with the spring constant
*k*, not stretched at first. Simulate the motion of the spring and
mass under the effects of spring and gravitational forces. Assume the
mass is *5 kg* and *k = 15 kg/s^2*. Then, set the mass to
be *10 kg* and *k = 20 kg/s^2*.

For both problems, you'll need to write *at least*
two functions (Euler's method vs.
Mid-point or 4th order Runge-Kutta) for integration and compare their numerical
accuracy and stability. Which function is more accurate? Which one
is more stable? Which one is more efficient?

**This assignment will be graded based upon: **