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Mechanics

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10 Sep 2007 21:11:44 IST

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a stone is projected from the ground in such a direction so as to hit a bird on the top of a telegraph pole of height h and attains the maximum height 2h above the ground.if at the instant of projection,the bird were to fly away horizontally with a uniform speed find the ratio between the horizontal velocities of bird and the stone,if the stone hits the bird while descending.

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Somye---- elegance personified

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Joined: 19 Jul 2007

Posts: 107

11 Sep 2007 07:46:52 IST

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see this is easy

let velocity of stone be u and that of bird be s and time of hitting be t

then horizontal distance travelled by stone is ucos

and distance travelled by bird is st

since st=ucos

s=ucos

u/s=1/cos

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eesha shirke

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Joined: 9 Sep 2007

Posts: 4

11 Sep 2007 16:47:30 IST

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hey am not satisfied with ur ans as the final answer given is 2/root of 2+1

shahid kumar

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Joined: 23 Aug 2007

Posts: 25

11 Sep 2007 17:57:53 IST

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I have used the notation used by the previous student.it was aimed to hit the bird so it passes through the top of pole but there is no bird so hits at the same hieght but and the other one in its trajectory.the previous solution is wrong as st=vt+d as it is not fired from the same x it can be solved this way alsobut see the shortest one. solution is st(time till going to the hit point)=vt₁(time taken to gofrom the top of the pole to hit point) as both are the distance between top of pole and the hit point.so s/v= t₁ /t. now t is time taken to go till the second h height.vertical speed at second h height is -

V²(vertical initial)-2gh and V is

2gx2h so you get .vertical speed at second h height is -

2gh( - ) for down wards. -

2gh=

4gh -gt so t is (

2+1)

h/g and t is time taken to go till the second h - time taken to go till the first h(whichcan be obtained in a similar manner) so t comes to be 2

h/g. so t₁ /t.=2/ (

2+1).I hope yr. satisfied..

Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5153

21 Sep 2007 10:23:51 IST

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Sorry for delayed reply, but shahid your answer is perfect. Well done

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