Physics Course/Projectile Motion

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Projectile Motion[edit]

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 t[edit]

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

and the direction is given by

Time of flight[edit]

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


Horizontal range[edit]

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

Maximum height[edit]

The maximum height is given by

where h is the initial height

method 1 - completing the square[edit]

method 2 - by symmetry[edit]

method 3 - by calculus[edit]