Projectile in 3 dimensions I need a little bit help in solving problem involving projectile motion in 3-dimensions. In 2D i can solve by using range formula or by substituting time from horizontal direction into vertical component but i don't understand how to solve it in 3-dimension. Here is an example if anyone can give an example it would be a great help.
Consider a 3-dimensional space, i.e. a space with an $x$, $y$ and $z$ axis. A projectile is thrown up at an initial velocity $v_0$ from a height $h_0$. The acceleration is constant.
No i don't understand how to solve it for (speed and specially position) in 3-dimension.
 A: Motion in the x, y and z directions is independent. You can write down 3 separate equations of motion for each direction in 3D, just as you can in 2D, using time as a parameter. Instead of one horizontal direction, you now have 2 separate horizontal directions. 
The initial velocity in each direction is the component of the launch velocity in that direction. The only difficult aspect of this is that the launch angle is usually given between the ground plane (xy) and the initial direction of the projectile. If this angle is $\theta$ and looking down this vector makes an angle $\phi$ with the x axis then the initial components are $u_x=u\cos\theta\cos\phi, u_y=u\cos\theta\sin\phi$ and $u_z=u\sin\theta$, where $z$ is the vertical axis. That is, first project the launch velocity onto the horizontal plane (xy) then resolve this into x and y components. On the other hand, the initial velocity vector might already be given in terms of its x, y, z components, then there is no need to resolve the velocity vector.
Alternatively, you can choose a new horizontal axis w along the direction which the projectile takes in this plane. Then you have a familiar 2D problem with $v_w=u\cos\theta, u_y=u\sin\theta$. Horizontal positions x, y are the components of w, viz. $x=w\cos\phi, y=w\sin\phi$.
