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Projectile Motion

An object that is in flight after being thrown (projected) is called a projectile.
e.g., Football, a cricket ball, a baseball or any other object.
The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motions.
One component is along a horizontal direction without any acceleration and the other along the vertical direction with constant acceleration due to the force of gravity.
It was Galileo who first stated this independency of the horizontal and the vertical components of projectile motion.
In our discussion, we shall assume that the air resistance has no effect on the motion of the projectile. Suppose that the projectile is launched with velocity Vo that makes an angle θ0 with the x-axis.
After the object has been projected, the acceleration acting on it is that due to gravity which is directed vertically downward:

Or, ax = O, ay = -g
The components of initial velocity are:
If we take the initial position to be the origin of the reference frame as shown in figure, we have:
xo = 0, yo = 0
Equation (viii) gives the x-, and y- coordinates of the position of a projectile at any time t in terms of two parameters-initial speed and projection angle θo.

Notice that the choice of mutually perpendicular x-, and y-directions for the analysis of the projectile motion has resulted in a simplification. One of the components of velocity, i.e. x-component remains constant throughout the motion and only the y-component changes, like an object in free fall in vertical direction.

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