Projectile motion - vertical and horizontal velocity (two components) #3

Projectile motion involves vertical and horizontal components of velocity. It is important to understand that the two are independent of each other. But what is projectile and is there what is a good example.
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Well, a projectile is any object thrown by applying force such that it comes under the force of gravity and experience resistance of the medium in which it travels. An example of projectile motion would be a ball thrown upward in the air at any angle such that falls under the influence of gravity.
Imagine what will happen to the ball if it is shot at an angle theta from the ground level. This then is called a projectile motion. Let us try to examine what is happening to ball as it comes out of the cannon. The moment it starts it has a velocity Vo at an angle theta. This velocity is making the ball move to the vertically up and also horizontally to the right.
Vertical Movement - The initial velocity of the ball in the vertical direction is Vo Sin (Theta). You will notice that there is force of gravity acting on the ball in vertical direction. Thus the vertical component VoSin (theta) will constantly reduce in the vertical direction till it reduces to zero. Infact the ball will follow all rules of motion applicable to any body moving in vertical direction under force of gravity.
Horizontal Movement - You would see that gravity is acting on the ball in vertical direction but there is no force acting on the ball in horizontal direction. If there is no force acting in the horizontal direction, there is no acceleration acting on the ball. There is no reason for velocity of the ball to change. Hence the velocity of the ball continues to remain the same as the initial velocity in the horizontal direction.

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A projectile is fired horizontally with velocity U. Show that its trajectory is a parabola. Also, obtain the expression for its (i) time of flight (ii) horizontal range and (iii) velocity at any instant. And A projectile is fired upward at an angle Ɵ with the vertical with velocity U. Show that its trajectory is a parabola. Obtain expressions for (i) maximum height attained (ii) time of flight. Sir I had a doubt as to what these two questions mean.. Love from India

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Before reaching max height, the horizontal component of velocity vector is acting upwards, hence taken positive. But after crossing the maximum height, the horizontal component of velocity vector is acting downwards. So it should be taken negative right? (i.e +V during upwards motion, and -V during downwards motion?)

[@TheScienceCube]

You mean the vertical component?

[@karunareddy6966]

@@TheScienceCube yep

[@karunareddy6966]

@@TheScienceCube Yeah, after crossing max height, it should be like (-V) = (Vo) + (-g)t. right?

[@TheScienceCube]

@@karunareddy6966 ..but you have written horizontal. Yes that is entirely correct. See the notation that we usually follow is that any vector pointing in direction of +y axis is positive and any in +y direction as negative. That is the reason g is always negative.

[@karunareddy6966]

Hmm, I strictly support this point. But many educators disagreed saying it will eventually become negative. SO summary is : for upwards motion : Vertical component is : V = v0sin theta - gt for downwards motion : Vertical component is : (-V) = v0sin theta - gt but, it many reference books like many famous books of kinematics generally prefer saying Vertical component is : V = v0sin theta - gt for whole projectile path. why is that so?

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[@sugar6467]

why do we take components of velocity in projectile motion?

[@TheScienceCube]

The components are taken because the projectile moves in 2 dimensions. Hence resolving into components helps us study the motion better. Luckily the motion in vertical direction and that in horizontal direction are totally independent

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[@getsomeairr]

I am confused rn. I guess somewhere I read something like 'the component of velocity normal to the force remains unchanged'. Is this in any way applicable to this video as well? If yes, how? It'll be really great if you replied.

[@TheScienceCube]

That's right Nupur. Since the force here is gravity that acts vertically down, the velocity in horizontal direction should not be effected at all and therefore does not change. Does that answer your question?

[@getsomeairr]

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