If an object is thrown vertically upwards, its subsequent motion can be predicted using the equations of
motion for bodies moving with uniform acceleration (click here for worked
example of this). 



If an object is thrown at some other angle, as shown
below, we can still predict
its motion using the same equations, as long as we use the vertical and
horizontal components of the initial velocity of the object. 





The vertical component changes uniformly because of gravity. 

The horizontal component remains constant (if we ignore the
effects of air resistance, which we will do here... because it makes things
easier!). 



These two facts combine to give a trajectory which is a parabola. 



To calculate 

 the time taken (t) to reach maximum height


 the maximum
height reached 

we use the equations of motion (v = u + at, s = ut + ½at² etc) but the velocities
"u" and "v" now refer to the
vertical components of the initial and final velocities. 



NB The total time "in the air" is, of course, simply 2t 



To calculate the range of the projectile, first find the total time in the air
and then use the fact that the horizontal component of velocity is
constant. 



(click here for worked
example of this) 
