Problem 4: A projectile of mass m = 10 kg is launched with initial velocity $V_0$ = 900 m/s
at the angle $\theta$ = 30°. The motion of the projectile on the plane (x, y) is affected by the
aerodynamic drag force and gravity force and is described by the equations of motion
$mx'' = -\frac{1}{2}C_D\rho A\sqrt{(x')^2 + (y')^2}x'$
$my'' = -\frac{1}{2}C_D\rho A\sqrt{(x')^2 + (y')^2}y' - gm$
where A=30 cm², $C_D$ = 2 is the projectile drag coefficient, $\rho$ = 1 kg/m³ is the density of air
in Earth atmosphere, and g=9.81 m/s² is the acceleration of Earth's gravity field.
1. Re-write equations of motion in the form of 4-dimensional fundamental system
2. Formulate the initial conditions for this system
3. Solve the problem with the ode45 solver.
4. Find trajectory of the projectile until the time when it hits the ground and plot it on
the plane (x, y).
5. Find the distance of flight D of the projectile (along axis x) and maximum height of
trajectory H (along axis y).
