PHYSICS: Projectile Motion

Projectile motion refers to the motion of an object projected into the air at an angle. A projectile is an object upon which the only force acting is gravity. Objects launched are called projectiles.

History:

Niccolo Tartaglia shows it was realized that projectiles actually follow curved path. Yet no one knew what that path was, until Galileo Galilee. First, he reasoned that a projectile is not only influenced by one motion, but two. The motion that acts vertically is the force of gravity that pulls an object towards the earth at 9.8 m/s². While having this motion, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to Galileo’s principle of inertia. This two independent motions of him work together to create a precise mathematical curve – mathematical shape, a shape from Greeks called parabola.

Parabolic motion has the following properties.

1. They are under constant acceleration.
2. There, exists a non-zero component which is perpendicular to the acceleration so as to produce a parabolic path. If this condition is not satisfied, the motion is actually a linear motion. 

Basic Equations:

Horizontal velocity = u cos θ

Vertical velocity = u sin θ

The horizontal and vertical displacements of the objects are:

            (x) Horizontal displacement at time =  

            (y) Vertical displacement at time =

To find the maximum height:

So from dy/dx = 0, we get u sin θ – gt = 0

Sub (1) into the vertical displacement equation:

Equation of Trajectory:

From above, we know that:

            Horizontal motion (x) =

                                 

            Vertical motion (y) =  

                   

Eliminating t, we get

                          

This equation can be transformed to a quadratic equation in tan a

FORM OF EQUATIONS	USES
	1.        Find out the position of an object at a particular time. 2.      Find out the time taken for an object to travel to particular position.
	1.        Find out the y-position by given other condition. 2.      Find out the x-position by solving this quadratic equation.
	1.        Find out the angle of projection. 2.      Determine the minimum velocity of projection to clear an obstacle.

Source: www.library.thinkquest.org/