Projectile Motion

                                  A projectile is a body which is given an initial velocity at a given angle to the base - and it then follows a trajectory determined by the effect of  gravitational force and air resistance . Think of the trajectory of a ball thrown into the air or a cannon ball which is shot . 

 << Click here to launch the Projectile Motion visualization applet >> 
   Mini - Screencaptures : 

   1. Trajectory of a projectils thrown at an angle X at a velocity V . 
    2. Trajectory of projectiles with Air Resistance . 
    3. Trajectory of a projectile on an inclined surface . 
 Let a ball be thrown with initial velocity V at an angle X to the horizontal . 

 Horizontal Component of Velocity = V cos X 
 Vertical Component of Velocity = V sin X 

 There is no acceleration in the horizontal direction; acceleration in vertical direction is (downwards)  g   : where g is the acceleration due to gravity .

  y - y0 = (V sin X) t - 0.5*g*(t^2)
  x - x0 = (V cos X) t
  y = x(tan X) - (x^2)*g / ( 2 * ( V cos X ) ^ 2 )
  Time to reach ground = V sin X / g
  Time to reach the highest spot = 2 * V sin X / g
  Range of projectile = ( V ^ 2 ) * (sin 2X) / g
  Max Height = ( V sing X) ^ 2 / 2g

  This is an example of a parabolic curve . 
 Now if we assume air resistance there will be retardation in the X direction . 
  The Horizontal component of velocity as a function of time will now be V cos X - rt 

   Where r is the retardation due to air resistance . 
   << Click here to launch the Projectile Motion visualization applet - 1 >> 

In this applet ( the gray-green one ) you can adjust the 1) Starting Velocity 2) Angle at which the projectile is thrown 3) Angle at which the base surface is inclined . This is zero by default for a flat surface .  

<< Click here to launch the Projectile Motion visualization applet - 2 >> 

In this applet ( white background ) you can experiment with different projectiles thrown with different velocities and observe the effects of retardation due to air resistance . Multiple trajectories can be compared together .

Projectile Motion on a flat Surface 

Projectile Motion on an Inclined Surface 

Projectile Motion with Air Resistance 

Prashant Bhattacharji,
Jul 7, 2011, 6:19 AM