Elliptical cage

A ball is thrown with some velocity v v along MA inside an elliptical cage the ball strikes the wall of the cage and rebound and again strike at B.

Answer the following questions

1) It will strike A 'N' times (excluding 1st one)

2)It will strike B 'S' times (excluding 1st one)

3)It always pass through a fixed pt between every 2 collisions.

1)'E'=0(if above statement is true)

2)'E'=1 (if above statement is false)

4) It will follow the path at t---->00

1)along major axis('P'=1)

2)along minor axis('P'=2)

3)along MA ('P'=3)

note

1)coordinates of m(-3,0)

2)This one is original

'N+S+E+P'=?

7 5 3 \infty 6 1 2 4

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2 solutions

Mayank Singh
Apr 26, 2016

You probably got this one from FIITJEE's FULL TEST dated 25 April 2016

It had a 90 percent similar question

no i have not i swear.

aryan goyat - 5 years, 1 month ago

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Ok relax, I believe u ... It may just be a co incidence

Mayank Singh - 5 years, 1 month ago

it is total mine i just created it using the properties of ellipse

aryan goyat - 5 years, 1 month ago

i am 12(this year) so how could i.

aryan goyat - 5 years, 1 month ago

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your profile says 17

Mayank Singh - 5 years, 1 month ago

does that mean 12th pass

aryan goyat - 5 years, 1 month ago
Aryan Goyat
Apr 25, 2016

the credit to this solution goes to @Aniket Sanghi he could not post the sol because of some reason. Firstly, since e=1 the process would go till infinity

Secondly, by reflection property of ellipse after reflection it will pass through focus (in direction of reflection) every time (alternate). so on careful observation ,you will see that the ball tends to come to move on major axis..

Explanation : after reflecting from B it will pass from M before next collision , then after this collision it will pass through second focus before the next collision ....then after this collision it will again pass through M and similary after....at the end it will tend to come to move in major axis!

which all are correct ?

Aniket Sanghi - 5 years, 1 month ago

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oh got my mistake ,, you told 1 for false , i took 1 for true{binary:(} , by the way my solution was correct , i am happy to that

Aniket Sanghi - 5 years, 1 month ago

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easy if you know properties 17 views 2 attempts 0 solvers please post solution

aryan goyat - 5 years, 1 month ago

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@Aryan Goyat i cant , i didnt got it correct , officilly i am not allowed

Aniket Sanghi - 5 years, 1 month ago

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@Aniket Sanghi write it in reply i will add and give as your contribution

aryan goyat - 5 years, 1 month ago

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@Aryan Goyat My solution is very simple ...

Firstly, since e=1 the process would go till infinity

Secondly, by reflection property of ellipse after reflection it will pass through focus (in direction of reflection) every time (alternate). so on careful observation ,you will see that the ball tends to come to move on major axis..

Explanation : after reflecting from B it will pass from M before next collision , then after this collision it will pass through second focus before the next collision ....then after this collision it will again pass through M and similary after....at the end it will tend to come to move in major axis!

Aniket Sanghi - 5 years, 1 month ago

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@Aniket Sanghi yep could you also prove that mathematically

aryan goyat - 5 years, 1 month ago

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@Aryan Goyat I won't like to! Sorry!(it would take time to write it)

Aniket Sanghi - 5 years, 1 month ago

@Aryan Goyat your imagination is brilliant! ( Nice Question!)

Aniket Sanghi - 5 years, 1 month ago

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