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Motion in A Plane

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Physics Part I

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Class 10 Class 12
A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m/s to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take g = 10 m/s2)

Velocity of shell is, u  = 600 m/s

Velocity of fighter plane is, v = 720 km/hr = 200 m/s



Let the shell be fired at angle θ with vertical.

To hit the fighter plane, the horizontal 
component of muzzle speed should be equal to the velocity of plane.

i.e.               space space space space space straight v equals straight u space sinθ          

rightwards double arrow              200 space equals space 600 space s i n space straight theta

rightwards double arrow               sinθ space equals space 1 divided by 3


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The maximum height attained by the shell is,

              straight H equals fraction numerator straight u squared sin squared left parenthesis 90 minus straight theta right parenthesis over denominator 2 straight g end fraction

                 equals fraction numerator left parenthesis 600 right parenthesis squared space s i n squared left parenthesis 70.53 right parenthesis over denominator 2 cross times 10 end fraction
equals 15995 space straight m 
That is, 
             space space straight H asymptotically equal to 16 space km

Therefore the minimum altitude for safe flight is 16km.


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