Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2014-09-16 19:36:58

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

projectile

A particle is projected over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base.If

and
be the base angle and
the angle of projection , prove that
.


friendship is tan 90°.

Offline

#2 2014-09-17 00:11:14

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

hi Niharika,

I haven't had a chance to follow this through yet, but here's how I'd begin:

horizonally

vertically

So now you have a quadratic in x.  You can substitute in (0,0) ; (a,h) and (a+b,0)  where

h = a.tan(alpha) = b.tan(beta) and aim to eliminate a, b, g and  v.  Although that's four unknowns and only three equations, you can think of g/2v^2 as a single variable, so you should be left with an expression connecting the three tangents.  smile

EDIT:  Whoops the first equation would be 0 = 0 which doesn't help much.  shame  I'd better try this properly.

FINAL EDIT:

It does work.  From the (a,h) equation re-arrange to make k (=g/2v^2)  the subject and substitute this into the (a+b,0) equation.

Use the a and b equations to remove a and b from the equation.  Bonus: the h terms all cancel.  smile

Simplify what's left to get the required result.  smile

Bob

Last edited by bob bundy (2014-09-17 00:31:26)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#3 2014-09-17 00:21:37

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: projectile

Can I have a diagram, niharika?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#4 2014-09-17 00:38:05

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

EVKqXg8.gif

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#5 2014-09-17 01:26:48

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: projectile

Which is alpha, beta and theta?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

#6 2014-09-17 02:24:30

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

Alpha is the angle in the left hand triangle so tan alpha = h/a

Beta is the same for the right hand triangle so tan beta = h/b

Theta is the angle to the horizontal at which the projectile is launched.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#7 2014-09-17 03:44:07

Olinguito
Member
Registered: 2014-08-12
Posts: 649

Re: projectile

Bob has worked out

So the length of the base of the triangle is
.

We can rewrite equation [1] as

From the diagram in post #4

Also, substituting (x,y) = (a,h) into [2],

Cancel the d, simplify, and you should get the answer.


Bassaricyon neblina

Offline

#8 2014-09-17 04:01:35

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Re: projectile

thank you so much for such  simplified answers.
It is really very helpful(because my brain is not working right now and I have my Physics exam tomorrow). smile


friendship is tan 90°.

Offline

#9 2014-09-17 05:48:38

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

Good luck with the exam.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#10 2014-09-17 18:55:19

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Re: projectile

It's over now.

and I couldn't make this one:-
Q.A ball rolls off the top of a stairway with a horizontal velocity u.If the steps are h meter high and b meter wide, show that the ball will just hit the edge of nth step if

.


friendship is tan 90°.

Offline

#11 2014-09-17 19:59:35

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

hi Niharika,

Same method as the earlier one:

horizontally

vertically

+ as we want to measure downwards.

If you substitute in that expression for t, cancel an 'n', and re-arrange, it comes out in a few lines.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#12 2014-09-18 00:30:46

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Re: projectile

hmm, so it was simple.
thanks again bob. smile


friendship is tan 90°.

Offline

#13 2014-09-18 01:09:28

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

No, it was really hard.  But I'm a brilliant teacher so it now seems simple.  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#14 2014-09-18 16:49:42

niharika_kumar
Member
From: Numeraland
Registered: 2013-02-12
Posts: 1,062

Re: projectile

Yes you are.
Your explainations have always proved to be very beneficial. smile


friendship is tan 90°.

Offline

#15 2014-09-18 19:21:54

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

Re: projectile

I did say that as a joke, so thank you for your reply.  smile

Bob

Last edited by bob bundy (2014-09-18 19:22:20)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

Board footer

Powered by FluxBB