2nd Order Ordinary Differential Equation

How do you solve the following 2nd order ODE

so this question describes the motion of an object in 3-D space

r vector represents the position of an object a vector is an acceleration vector caused by drag g vector simply represents the gravitational acceleration where g_z = -9.8

r(0) is given by

and r'(0) or v(0) is given by

* Now here is my question *

Assuming that drag is 0 (thus, a vector simply reduces to 0) and given initial conditions above

How can you find the time(t_I) at which the object hits the ground (r = 0)

and how can you express the position and velocity of this object as functions of time?

Can anyone provide the MATLAB code to solve these problems?? :P

Answer 1

[Torsten]

If the drag is zero, the general solution is

x(t) = x(0) + vx(0)*t + gx/2*t^2
y(t) = y(0) + vy(0)*t + gy/2*t^2
z(t) = z(0) + vz(0)*t + gz/2*t^2

Best wishes

Torsten.