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CBSE Class 11-science Answered

A bullet fired at an angle of 30° with the horizontal hits the ground 3km away.By adjusting the angle of projection and keeping the muzzle speed same show if one can hit a target 5km away.
Asked by tps.mjmdr | 09 Jul, 2018, 09:47: PM
answered-by-expert Expert Answer
Range R of the projectile is given by,   begin mathsize 12px style R space equals space fraction numerator u squared sin space 2 alpha over denominator g end fraction............ left parenthesis 1 right parenthesis end style
where u and α are velocity and angle of projection. g is acceleration due to gravity.
 
velocity of projection  u that can be obtained from (1) is,  begin mathsize 12px style u space equals space square root of fraction numerator R cross times g over denominator sin space 2 alpha end fraction end root space equals space square root of fraction numerator 3000 cross times 9.8 over denominator sin space 60 end fraction end root space equals space 184.25 space m divided by s
end style
From eqn.(1), it can be seen that range R will be maximum when α = 45º and
maximum range Rmax = (u2 / g ) = (184.25×184.25)/9.8 = 3464 m
 
Hence by keeping the same muzzle speed u, one can not hit a target which is 5 km away
just by changing projection angle.
Answered by Thiyagarajan K | 09 Jul, 2018, 11:28: PM
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