| 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