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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12
Show that the ratio of the horizontal range to the maximum height attained by projectile is equal to 4 cot straight theta and is independent of speed of projection.

The horizontal range attained by projectile projected with velocity u at angle θ is, 

                   straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction 

Maximum height attained by projectile projected with velocity u at angle θ is, 

                     straight H equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction
The ratio of horizontal range to maximum height is given by, 

    straight R over straight H equals fraction numerator straight u squared sin space 2 straight theta over denominator straight g end fraction cross times fraction numerator 2 straight g over denominator straight u squared sin squared straight theta end fraction equals 4 space cotθ

Hence, the result proved. 
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Give three examples of scalar quantities.

Mass, temperature and energy
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Give three examples of vector quantities.

Force, impulse and momentum.
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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. 


814 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

What is a vector quantity?

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