Motion in A Plane

Physics Part I

Physics

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A projectile is projected with velocity u at an angle θ with horizontal. Discuss the trajectory of projectile. Also find the velocity of projectile at any instant.

Let us consider a projectile is projected with velocity 'u' at angle 'θ' with horizontal direction from a point on the ground.

Let the point of projection be origin, right direction is positive direction of X-axis and vertically upward direction is positive direction of Y-axis.

Equation of trajectory:

Break the components of velocity and acceleration due to gravity in horizontal and vertical direction.

x

a

Motion along horizontal direction:

...(1)

Motion along vertical direction:

...(2)

Eliminating t from (1) and (2),

This the required equation of trajectory.

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

Velocity of projectile:

Let at any instant, be the velocity of the projectile making an angle with the horizontal.

i.e.,

u_{x} = u cos , u_{y} = u sin

a_{x} = 0 , a_{y} = -g

Now,

v_{x} = u_{x} + a_{x}t , v_{y} = u_{y} + a_{y}t

Therefore,

v_{x} = u cos , v_{y} = u sin - gt

The velocity f the projectile is given by,

v =

Angle pf projection is given by, tan =

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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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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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