Kinematics _ Projectile motion

So...

There is that one time in every student's life when you are fed up. You just want to bash your head against the wall. You are cursing and scolding every physicist who has ever walked on earth because their theories are the reason your head is exploding.

You want to take your physics book and just throw it out of your window.

Now, what If I said there is a physics theory for that. Yup, you will be using physics to throw your physics book out of the window ( Rubbing salt on the wound , isn't it?)

(P.S - You might think, Wait, The writer who goes on and on about physics in her blogs is giving this intro? Let me make this clear, I absolutely love physics, adore it, totally, but there are some times when everything just stops making sense and you have to let it out. and for the record, I am more of a set -the-book-on-fire kind-of gal 🙃)

Now, back to the students who are standing with their heads reeling , the immortal life of a physics book balancing in your hands, Let me explain the perfect way to throw your physics book using physics.

(Meaning of the terms in the diagram

U = intial velocity ( aka the desperation you were in, at that time )

R = Range ( Total distance covered)

H = Height (Maximum height reached by the object )

V = velocity at an instant

g = the one and only GRAVITY! )

The first step to start the calculation is to break the inital velocity into its components ( i.e the initial velocity along x and y axis )

The same technique is used to find the velocity vector along y axis too

Now, to the derivations

(To all those who are wondering -- What is displacement?! -- It is the final position minus the intial position , and in this case as the object starts from ground level and reaches there at the end , displacement is zero)

If you want to throw your book as far from you as you can but with the same energy, we need the 2 theta part to be maximum. We know that the maximum value of sin is always 1

hence,

sin 2θ = 1

sin 2θ = sin 90

2θ = 90

θ = 45 degrees

Throw it at 45 degrees to get it as far from you as you can ( I know, throwing while using the protrator will be hard , well, but we still want the maximum effect and damage ,right?🙃)

- Important things to notice here is that

1) Gravity is always constant and acting downward , hence there is no acceleration on the horizontal place ( along X axis) hence 'x' component of velocity remains same throughout

2) At maximum height, the object doesn't go up anymore ( *duh* ) hence the vertical component ( y component) of velocity at that point is ZERO

Now, to sum up the entire projectile , we have

This equation can also be expressed in terms of Range :- ( I mean , why not?)

Okay, so you were in an open ground when throwing in this case, Let's consider another half our reader, who live or have their class in the upper floors -- they are not present in the ground level

CASE.1 -- When you decide to throw the object up from a height

CASE .2 -- When you throw it down from a height

Now, what if a person was standing below when you threw your book and it hits them square on their head, What will be the velocity with which it hits the poor guy?

From this equation we can conclude that the final velocity it falls does not depend on the angle with which you throw, the person will have the same amount of headache for any direction you throw it in (And if the book is something like HC Verma, then make sure you call the Ambulance immediately 😬)

That was the complete research on the perfect ways of throwing your physics book using physics. Physics (digging its own hole) explains copious methods to throw ( or chuck as used in our colloquial language).

This kinda shows us how every single thing in this world uses physics, from scientists who send rockets to space to a very annoyed student.

Now keeping up with our tradition...