# Need derivation of projectile motion

1. Sep 11, 2011

### piyush3dxyz

Hey i need derivation of projectile motion..
All four equation..
including range,height,X-axis distance,y-axis distance..

2. Sep 11, 2011

### Staff: Mentor

Try this: http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html" [Broken]

Last edited by a moderator: May 5, 2017
3. Sep 11, 2011

### piyush3dxyz

thx a lot sir....
regards piyush....

Last edited by a moderator: May 5, 2017
4. Sep 11, 2011

### BruceW

A projectile has constant acceleration downwards of g (roughly equal to 9.81m/s^2). And it has zero acceleration horizontally.

Since the acceleration is completely specified, we can use integration to find the laws of motion. Using z=upward and x being horizontal:

$\ddot{z}=-g$ and $\ddot{x}=0$. Now using integration on both equations individually:
$\dot{z} = \dot{z_0} -g(t - t_0)$ and $\dot{x} = \dot{x_0}$ (where the subscript zero are constants - i.e. boundary conditions). So now we integrate the equations again to get:
$z = z_0 + \dot{z_0}t -\frac{1}{2}g(t - t_0)^2$ and $x = x_0 +\dot{x_0}t$

These are all the laws of motion necessary. If you get a question that tells you the initial angle an object is fired at, then that gives you the ratio of the horizontal and vertical initial speeds. And if you get a question asking where an object ends up landing, then often you can solve for the vertical motion to get the time, and then use the time in the horizontal motion equation to get where it ends up landing.