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Physics Part I

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Class 10 Class 12
There are two angles of projection for which horizontal range is same. Prove that the sum of maximum heights for these two angles is independent of angle of projection.

Given, horizontal range is same for two angles of projection. 

The angles are θ and 90°–θ.

Maximum height H1 for angle projection θ is,

                     straight H subscript 1 equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction 

Maximum height H2 for angle projection 90°–θ is, 

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

Now, sum of maximum height is,  

  space space space space space straight H subscript 1 plus straight H subscript 2 equals fraction numerator straight u squared sin squared straight theta over denominator 2 straight g end fraction plus fraction numerator straight u squared cos squared straight theta over denominator 2 straight g end fraction equals fraction numerator straight u squared over denominator 2 straight g end fraction   

Hence the result.

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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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Give three examples of vector quantities.

Force, impulse and momentum.
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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 scalar quantities.

Mass, temperature and energy
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