Projectile lovers (The answer is really short)

A projectile is fired from height h with a speed V0.What is thje angle of projection so that range is maximum ?

19 Answers

23
qwerty ·

R^{2}=h^{2}+\frac{2v^{2}[sin\theta \sqrt{R^{2}-h^{2}}+hcos\theta ]cos\theta }{g}

i got something like dis

1
Hodge Conjecture ·

mine ans. is also same.....since cos-1x + sin-1x = pi2....using this,,we will get the same ans......

23
qwerty ·

it is the same thing to wat i hav written in #11

also see http://www.targetiit.com/iit-jee-forum/posts/mechanics-doubt-17302.html [3] [3] .... same result

1
pritishmasti ............... ·

thnx satyapriya...nice question

1
SatyaPriya Ojha ·


There is so much literature on projectiles..If you guys are interested I can post some more..

1
Hodge Conjecture ·

finally i am getting....
\large required\,angle=\frac{\Pi }{4}-\frac{1}{2}\sin^{-1} (\frac{gh}{gh+v_{0}^2})

1
Hodge Conjecture ·

so using above relation we can find angle \phi in terms of h and u.....
then we can apply the condition for maximum range on inclined plane......and find the required angle ..............

1
Hodge Conjecture ·

sir i hv edited my post......in the given eq. \phi is the inclination of the assumed inclined plane with the horizontal....its not the inclination of V0 with the horizontal....

62
Lokesh Verma ·

born your expression seems to give infinity as the answer....??

are you applying the whole thing correctly?

1
Hodge Conjecture ·

\large R_{max}=\frac{v_{0}^2}{g(1-sin\phi ) }

write eq. for range down an inclined plane nd then find its max. value.....u will get the above equation.

don't worry about height h given in the problem......u can easily relate 'h' with the above eq. by trigonometric relations.....

i.e in the given problem we can write...
\large \frac{h}{sin\phi }= R_{max}

N.B→ in the above eq. \phi in the inclination of the imaginary inclined plane....

49
Subhomoy Bakshi ·

simple application of maxima and minima ...

vertical component of velocity =vosinθ

and horizonal component of velocity = vocosθ

where θ is the angle of projection with the horizontal axis!

now, applying principles of kinematics for constant and zero acceleration,

-h = (vosinθ)t - 12gt2

gives t = vosinθ±√vo2sin2θ+2ghg

now, range R= vocosθ.t = vocosθ.vosinθ±√vo2sin2θ+2ghg

now using derivatives as tool to find maxima, we fing maximum range related θ

by, ddθR=0
and, ddθ.ddθR<0

genius mathematicians help me out with this hefty mathematical part (to solve it un-erronously and easily if there is another way in their mind! :P)

But the question demands a short answer :(

62
Lokesh Verma ·

yup (enuf interfering in satya's post... :P) until he is around to reply.. or someone gives the right answer

23
qwerty ·

eqn of trajectory ?
ohh i didnt see that height h

62
Lokesh Verma ·

no qwerty... not this one.. thsi one is if it were a plane..

here we have a height "h"

The formula I was referring to was

y=x...-gx2... (still not able to figure out?)

23
qwerty ·

Range=vo2sin2A/g
A = angle of projection
hence for given vo,range will b max when sin2A = 1

so A = 45o

1
Hodge Conjecture ·

which formula sir?? :)

62
Lokesh Verma ·

I dont know if kaymant sir is hinting at the same..

but i guess there is only one formula to learn in this chapter called projectiles... [3]

1
Hodge Conjecture ·

this sum can be solved easily by assuming an imaginary inclined plane nd using the condition for maximum range down an inclined plane.........

66
kaymant ·

Why don't you use some properties of quadratic expressions?

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