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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.

The maximum height attained by the shell is,

That is,

Therefore the minimum altitude for safe flight is 16km.

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Give three examples of scalar quantities.

Mass, temperature and energy
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What is a scalar quantity?

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

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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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Give three examples of vector quantities.

Force, impulse and momentum.
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