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projectile motion has two c what is the path of a projectile ​

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Class 11>>Physics>>Motion in a Plane>>Projectile Motion>>Prove that the path of projectile motion

Question

Prove that the path of projectile motion in parabolic.

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Solution

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path of a projectile

let OX be a horizontal line on the ground and OY be a verticle line O is the origin for X and Y axis Consider that the projectile is fired with velocity u and making angle θ with the horizontal form the point ′O′ on the ground 

The velocity of projection of the projectile can be resolved into the following two components 

(i) ux=ucosθ,alongOX

(ii) uy=usinθ,alongOY

 As the projectile moves it covers distance along the horizontal due to the horizontal component ucosθ of the velocity of projection and along verticle due to the vertical component usinθ . let that any time t , the projectile reaches the point P , So that its distance along the X and Y axis are given by x and y respetively.

Motion along horizontal direction : it we neglect friction due to air, then horizontal component of the velocity  i.e. ucosθ will remain constant. thus 

Initial velocity along the horizontal ux=ucosθ

Acceleration along the horizontal ax=0

The position of the projectile along X-axis at any time t is given by 

x=uxt+21axt2

Putting ux=ucosθ and ax=0 we have 

x=(ucosθ)t+21(o)t2

or x=(ucosθ)t

or t=

Explanation:

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Answer:

The path followed by a projectile is called its trajectory.

Explanation:

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