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CBSE Class 11-science Answered

A particle A is projected with speed V1 from a point making an angle 60° with the horizontal. At the same instant, second particle B (lie in the same horizontal plane) is thrown vertically upwards from a point directly below the maximum height point of parabolic path of A, with velocity V2. If the two particles collide then the ratio of V1/V2 should be (A) 1 (B) 2/√3 (C) √3/2 (D) √3
Asked by shyamalimaborthakur89498 | 04 Aug, 2018, 08:39: PM
answered-by-expert Expert Answer
Maximum height h reached by the projectile is given by,  h  begin mathsize 12px style equals fraction numerator v subscript 1 superscript 2 space sin squared 60 over denominator 2 g end fraction space equals space 3 over 8 fraction numerator v subscript 1 superscript 2 over denominator g end fraction space................... left parenthesis 1 right parenthesis end style
Time taken t to reach maximum height is given by, t = begin mathsize 12px style equals space fraction numerator v subscript 1 sin 60 over denominator g end fraction space equals space fraction numerator square root of 3 over denominator 2 end fraction v subscript 1 over g space........................... left parenthesis 2 right parenthesis end style
Hence if collision has to be taken place between the projectile and second particle which is thrown vertically,
second particle should reach the height given in eqn.(1) in time given in eqn (2).
 
let us apply the formula " S = u×t - (1/2)×g×t2 "  to get this condition
 
begin mathsize 12px style 3 over 8 fraction numerator v subscript 1 superscript 2 over denominator g end fraction space equals space v subscript 2 cross times open parentheses fraction numerator square root of 3 over denominator 2 end fraction v subscript 1 over g close parentheses space minus space 1 half g open parentheses fraction numerator begin display style square root of 3 end style over denominator begin display style 2 end style end fraction fraction numerator begin display style v subscript 1 end style over denominator begin display style g end style end fraction close parentheses squared space.................. left parenthesis 3 right parenthesis end style
after simplification of eqn.(3), we get begin mathsize 12px style v subscript 1 over v subscript 2 space equals space fraction numerator 2 over denominator square root of 3 end fraction space end style
Answered by Thiyagarajan K | 05 Aug, 2018, 08:08: AM
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