In the last class I had taught you Kinematics related formulae.Today we are going to apply them.As both of you would remember most problems that we did last class were in one dimension.Projectile is just another problem but here the motion is in 2 dimension.What basically a projectile is?Let us say, Projectile is the name given to the trajectory that a particle follows when launched in earth's gravitational field.To give you example click on start and a particle would be launched.You can of course change the velocity and angle at which the particle is launched. The trajectory in which the paticle goes is what we call PROJECTILE.

Sir,that is a parabolic trajectory!!

Sir I didn't get it.Would you please explain it in detail?

Oh!dont get restless Rahul!.Lets begin from the scratch.Can you tell me the force that would act on it or rather can you please come on board and draw the free body diagram.If you remember I had told you that it is first for solving any problem of dynamics.

Let me think sir , yes I can draw. Thats the free body diagram of projectile sir.

Thats good ! This is the diagram that takes into account the forces acting on the system.Good ,keep up the good performance Rahul.Now lets see the effect of forces on the state of the system. The only force acting on it is the vertical force.Hence,regardless of the way you move the projectile moves(upwards,downwards or leftwards)the only force acting on it is gravitational force in vertical direction.All horizontal forces are absent which means that the horizontal component of the velocity would never change according to Newtons first law.

But what about air drag and the buoyancy force,the air drag may act in horizontal direction.

Ok!thats true.We are studying it under the assumptions that projectile is moving in free space and that the gravitational force is constant.

Sir, how can the force always act downward when the body actully moves upward or sideways.If an object is moving upwards there must be an upward force.Is'nt it!.Sir I mean "How in the world can object be moving moving upward if the only force acting upon it is downward???"

Try to think , it will take just a second for you to realize it yourself Remember what I had told you while teaching Newton's laws.I very well remember telling you that forces are only required to cause an acceleration (not a motion). This idea is simply not true; a force is not required to keep an object in motion. A force is only required to maintain an acceleration. And in the case of a projectile, that is moving upwards, there is a downwards force and a downwards acceleration; that is, the object is slowing down.I think it should be clear now.

Sorry sir for putting such a silly question.I have now got the point.

To further stress upon the point I would encourage you  to think of the motion in absence of gravity. the animation below would help you to grasp the concept.

I hope that's clear now. Now let me work on the mathematical details .Applying equation of dynamics you can say

x=v1*t

y=v2*t-0.5*g*t*t where v1 and v2 are the components in the respective direction.You can relate the to total velocity as v1=v*cos(theta) and v2=v*sine(theta). Eliminating t from both equation you can relate x and y as y=x*tan(theta)-0.*5g*x*x/(v*v*cos(theta)*cos(theta)).That is equation of a PARABOLA as Rohina pointed out initially.Important terms that you were getting in the initial demo are

1. Range Its the maximum horizontal distance traversed.

2.Max.Height Well that's easy. Its just the y-coordinate of the peak of the parabola.

3.Time of flight That's the time projectile took to complete the motion.

Having given the definition I expect you to derive the formula using the above equations and also other equations of kinematics if necessary.