Analysis Given the X and

  Y Components

We can make a preliminary analysis projectile motion provided that we are given the initial x and y components of a projectile's motion.  A fact that makes our analysis of projectile motion easier is the fact that the x and y components are independent of one another.  Meaning we can treat the motion of the particle moving horizontally and vertically separately.

From one dimensional vector analysis we know that general formula for velocity at a given time t, with an initial velocity v_o, and an acceleration a, is:

If we look at the horizontal component we ask our selves:

What affects the projectile in the horizontal direction?  The answer to this is nothing!  So the acceleration term can be removed and we are left with:

where v_xo is the initial horizontal component of velocity
and v_x is the horizontal component of velocity at some time later

From this equation we can see that the horizontal velocity of a projectile is constant under the assumptions we made earlier.

How about the vertical component?  Does anything affect it motion in the vertical direction?  Yes, acceleration due to gravity! Thus our general equation becomes:

Notice the +a is replaced with a -g.  The negative sign is needed if we choose the positive vertical direction as upwards.  Since the force of gravity acts downward we must use the negative sign.
 

The position of the projectile can be treated much in the same way:

Given the general formula for position from 1D vector analysis:

We can get the position in x from as: And the position in y as:

Notice that the x0 and y0 terms can be removed if we set our starting point to be at x=0 and y=0.
 

What If You Are Given an Initial Velocity and Angle?
 
 

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