Motion in A Plane

Physics Part I

Physics

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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/s^{2})

Velocity of shell is, u Â = 600 m/s

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

Let the shell be fired at angle Î¸ with vertical.

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

i.e. Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

The maximum height attained by the shell is,

Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â

That is,Â

Â Â Â Â Â Â Â

Therefore the minimum altitude for safe flight is 16km.

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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.Â

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What is a vector quantity?

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

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