30-04-10 Path of a projectile.

We all know that the path of a projectile is a parabola.
My claim is that if we threw a stone in real life (Even without air friction), it will not follow a parabolic path.

Am I correct? If yes, then what will be the path.

If no.. Think again ;)

20 Answers

1
archana anand ·

is it that projectile travel below escape velocity so its elliptical???[7]

62
Lokesh Verma ·

so far as sanchit has said abotu the trajectory being a conic is correct..

but after that depending on whether the speed of the stone is less, greater or equal to the escape velocity, the path will be elliptical, hyperbolic or parabolic..

Btw... humans cant throw stones at escape velocities [3]

hence a elliptic path

1
student ·

sanchit

mathrmatical proof :

since the energy is -ve the path has to be closed or bound

the conic section that is closed is ellipse

y conic section ??

its because the the polar form of trajectory is

which represents a conic section

how we got this equation ??

by solving the differential equation

and

** put u=r here

make subsituition r=1u

to get this equation

this simple harmonic motion and solution to this equation is

http://en.wikipedia.org/wiki/Orbit for more clarity

1
sanchit ·

bhaiiya iis der ne mathematical explanation...........

1
sanchit ·

is it right nooww......it feels so gr8 to be pinked :D:P

1
sanchit ·

1357
Manish Shankar ·

sorry guys my bad.. the diagram made me think that the image posted is that of the flattened earth due to the rotation of it.. [3]

So I said that that will cause the deviation..

But the explanation by sanchit (of course one needs to magnify it :D) is correct

1
Bicchuram Aveek ·

Kalyan ....school-e chol....bujhiye debo.

1
Bicchuram Aveek ·

sanchit is right......but nishant bhaiya wanted more explanation .... :-)

and kalyan is right too .... but not the answer to why ELLIPTCAL.

@Nishant Bhaiya : Can't think of anything else.........

@archana : if the object is thrown at a vel equal to the escape velocity........it's bound to follow a parabolic path.....and other conics for other cases.

it's because of v lesser than esc. vel. that it has to return to earth else it'll go out of reach and will be touching the earth just like a parabola.

1
sanchit ·

cant understand whts mistake in ma diagram to explain this one???????[7]

1
Philip Calvert ·

Elliptical

6
Kalyan IIT-K Beware I'm coming ·

@aveek cudnt understand ur soln...
@ nishant bhaiya

d fact dat it is nt in parabolic path -if i answer dat earth isnt a perfect sphere nd g isnt same thn .....or if i proceed wid d fact dat earth isnt a perfect sphere cud i reach sumwhere???
pls ans

1
Bicchuram Aveek ·

sir will the second statement in #10 be "deviation from parabolic path" ? If that's so then the reason is that gravity is not same everywhere .

Why ?

because it's launched with a velocity lesser than escape velocity....it won't go out of reach of earth...gravity will be attracting.....we first conserve angular momentum of the particle about it's initial position and the highest point and then conserve energy.....that's where we come into the idea of an ellipse.

But parabola is a special case of ellipse where e=1 ..... so when gravity is same at all points the foci meet and there's only one foci......so we get a parabola in the2nd case.

62
Lokesh Verma ·

sanchit.. that is a reason.. but you are missing out the major reason...

Infact that will be the reason of why there is a deviation from the elliptical path :D

62
Lokesh Verma ·

@Kalyan.. Gravity is not the same everywhere... Why?
@Kamalendu.... Is g ka direction perpendicular in the case of a projectile? I dont think so!

1
kamalendu ghosh ·

is it also bcuz.. g ka direction directly perpendicular nahin rahega and so vx will also get a retardation component of g???

so ellipse to cirlce(when velocity>escape vel) ????

6
Kalyan IIT-K Beware I'm coming ·

i dnt kno d second part though.........

6
Kalyan IIT-K Beware I'm coming ·

it is not parabolic coz gravity is not same evrywhere.....
can dis be a possible explanation??
nishant bhaiya pls check

62
Lokesh Verma ·

Good one.. ppl are cracking this one..

Other than Philip, can you justify

a) Why it is not parabolic (The easy part)
b) Why it is elliptical (The more difficult part)

1
hacker ·

agreed philip[1]

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