A fighter plane flying horizontally at an altitude of 1.5 km with a speed of 720kmhr passes directly overhead an anti aircrat gun.the gun fires a shell with a muzzle speed of 600ms at a certain angle with the horizontal at the instant plane is vertically above the gun.if the shell hits the plane find the angle made by the shell with the horizontal at the instant it was fired.

 

Asked by Tarun Rath | 13th May, 2014, 10:40: AM

Expert Answer:

begin mathsize 12px style h o r i z o n t a l space r a n g e space i s space g i v e n space b y space u cross times cos alpha cross times t space equals space R space equals v cross times t w h e r e space u space i s space p r o j e c t i o n space v e l o c i t y space o f space s h e l l space f i r e d space f r o m space g u n space w i t h space p r o j e c t i o n space a n g l e space alpha R space i s space h o r i z o n t a l space d i s tan c e space t h a t space e q u a l s space t h e space d i s tan c e space t r a v e l l e d space b y space p l a n e. space v space i s space s p e e d space o f space p l a n e space a n d space t space t i m e space t a k e n space t o space h i t space t h e space p l a n e s p e e d space o f space p l a n e space equals space 700 space k m divided by h r space equals space fraction numerator 700 cross times 1000 over denominator 3600 end fraction space equals space 200 space m divided by s s u b s t i t u t i n g space t h e space v a l u e s space f o r space u space a n d space R space w e space g e t comma space 600 cross times cos alpha space equals space 200  h e n c e space alpha space equals space cos to the power of negative 1 end exponent left parenthesis 1 divided by 3 right parenthesis space equals 70.55 degree end style

Answered by  | 5th Jan, 2018, 07:33: AM