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CBSE Class 12-science Answered

if a projectile is projected with a velocity u by making an angle x with the horizontal then at instant when its velocity y is right angle to its initial velocity x?
Asked by sbtech357 | 22 Jul, 2018, 01:30: PM
answered-by-expert Expert Answer
 
As shown in the figure, when the velocity vector v at point P becomes perpendicular to initial velocity vector u,
the resolved vertical component of v makes angle x with the velocity vector v.
 
hence we have, begin mathsize 12px style v subscript vertical line vertical line end subscript over v subscript perpendicular space equals space fraction numerator u space cos space x over denominator left parenthesis u space sin space x right parenthesis space t space minus begin display style 1 half end style g t squared end fraction space equals space tan x end style.................(1)
Eqn.(1) be re written as
begin mathsize 12px style u space cos squared x space equals space open parentheses u space sin squared x close parentheses space t space minus open parentheses 1 half g space sin x close parentheses space t squared t squared space minus space open parentheses fraction numerator 2 u over denominator g end fraction sin space x close parentheses t space plus fraction numerator 2 u over denominator g end fraction cos space x space c o t space x space equals space 0 space.......... left parenthesis 2 right parenthesis end style
 
eqn.(2) has solution :-  begin mathsize 12px style t space equals space u over g open curly brackets space sin space x space plus-or-minus space square root of 1 space minus space c o t squared x end root close curly brackets end style
we omit the solution with -ve sign, because physically it is not possible
( velocity vector v becomes perpendicular to initial velocity vector u, after the instant t = (u sin x)/g , when it reaches the maximum height,  not before)
 
Hence at that instant,  begin mathsize 12px style t space equals space u over g open curly brackets space sin space x space plus space square root of 1 space minus space c o t squared x end root close curly brackets end style  velocity vector becomes perpendicular to the initial projection velocity vector
 
Answered by Thiyagarajan K | 22 Jul, 2018, 03:41: PM

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