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

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°.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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.

EDIT: Whoops the first equation would be 0 = 0 which doesn't help much. 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.

Simplify what's left to get the required result.

Bob

*Last edited by Bob (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

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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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.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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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.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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

Bob has worked out

[list=*]

[*]

[/list]So the length of the base of the triangle is .

We can rewrite equation [1] as

[list=*]

[*]

[/list]

From the diagram in post #4

[list=*]

[*]

[/list]

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

[list=*]

[*]

[/list]

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

*Bassaricyon neblina*

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

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).

friendship is tan 90°.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

Good luck with the exam.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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

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°.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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

hmm, so it was simple.

thanks again bob.

friendship is tan 90°.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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

Yes you are.

Your explainations have always proved to be very beneficial.

friendship is tan 90°.

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,515

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

Bob

*Last edited by Bob (2014-09-18 19:22:20)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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