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Motion in A Plane

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Physics Part I

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Physics

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A projectile is projected horizontally with velocity u and allowed to fall only under gravity. Discuss the trajectory of projectile. 

Consider a projectile, which is projected with velocity 'u' in horizontal direction from a point at height h from the ground. 

Let origin be the point of projection. 

The right direction is positive direction of X-axis and vertically downward direction is positive direction of Y-axis.

The component of velocity and acceleration is resolved into horizontal and vertical components.

So, 
                    straight x subscript straight o equals 0 space space space space space space space space space space space space space space space space space space space straight y subscript straight o equals 0
straight u subscript straight x space equals straight u 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 0
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 straight a subscript straight y space equals space straight g 

Motion along horizontal direction is, 

     
space space space space space space space space space straight x equals straight x subscript straight o plus straight u subscript straight x straight t plus 1 half straight a subscript straight x straight t squared equals ut              ...(1) 

Motion along vertical direction is,

            straight y equals straight y subscript straight o plus straight u subscript straight y straight t plus 1 half straight a subscript straight y straight t squared equals 1 half gt squared         ...(2)

Eliminating 't' from (1) and (2), we get

                        straight y equals open parentheses fraction numerator straight g over denominator 2 straight u squared end fraction close parentheses straight x squared 

This is the required equation of trajectory.

Since the equation of trajectory is an equation of parabola, therefore path of projectile is parabola.

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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.
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

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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Give three examples of scalar quantities.

Mass, temperature and energy
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