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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.


What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.

Give three examples of scalar quantities.

Mass, temperature and energy

Give three examples of vector quantities.

Force, impulse and momentum.

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.