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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
A particle is projected with speed ‘u’ at an angle θ. Show that it will strike the ground with the speed u.
            

Let a projectile be projected with speed 'u' at angle 'θ' from O and strike the ground at P with velocity 'v'.

The projectile will strike the ground at P after time equal to the time of the flight.

Now, resolving the components of 'u' in the horizontal and vertical direction, we have

                   straight u subscript straight x space equals space straight u space cosθ space space space space space space space space space space space space space space space space space space space space space straight u subscript straight y space equals space straight u space sinθ
straight a subscript straight x space equals space 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight a subscript straight y space equals space minus straight g

Horizontal and vertical component is given by, 

         straight v subscript straight x equals straight u subscript straight x plus straight a subscript straight x straight t equals straight u space cosθ
straight v subscript straight y space equals space straight u subscript straight y plus straight a subscript straight y straight t space equals space straight u space sinθ space minus space gT space equals space minus straight u space sinθ 

Therefore magnitude of velocity at ground is, 

        straight v equals square root of straight v subscript straight x superscript 2 plus straight v subscript straight y superscript 2 end root space equals space square root of straight u squared space cos squared straight theta plus left parenthesis negative straight u space sin space straight theta right parenthesis squared end root 

           equals square root of straight u squared left parenthesis cos squared straight theta plus sin squared straight theta right parenthesis end root space equals space straight u         

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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.
865 Views

Give three examples of scalar quantities.

Mass, temperature and energy
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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.
835 Views

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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