Physics Course/Projectile Motion

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Projectile MotionEdit

Projectile Motion refers to any motion moving under the effect of gravity. This kind of motion is famous for its trajectory being in the shape of a parabola.


Analysis (two dimensional space)Edit

Suppose the object is projected at an angle   at a height h with an initial velocity of v with a gravity of g. When on Earth g will equal 9.8 m/s2.

The components of velocity in horizontal (x-) and vertical (y-) directions are:

 
 


By using  , The x- and y- coordinates of the object are

 
 

which are functions in time.

By eliminating t,

 

which shows that the trajectory is a parabola

Velocity at any time tEdit

The magnitude of the velocity at any time t is given by

 

and the direction is given by

 

Time of flightEdit

To solve for the time of flight, we set y(t)=0

 
  or  

Horizontal rangeEdit

After  , the x-coordinate of the object is given by

 

Maximum heightEdit

The maximum height is given by

 

where h is the initial height

method 1 - completing the squareEdit

method 2 - by symmetryEdit

method 3 - by calculusEdit