Motion in A Plane

Physics Part I

Physics

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A projectile is projected with velocity u at an angle Î¸ with horizontal. Find the time of flight, maximum height attained and horizontal range of projectile.

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

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

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

Â Â

Time of flight:

It is the time for which the projectile remains in air above the point of projection. It is represented by T.Â

The position of projectile at any instant in Y direction is given by,

The time of flight is the difference of instants when the Y position is zero.

i.e. Â Â Â Â Â Â

Â Â Â Â Â

Â Â Â Â Â Â Â and Â Â Â Â

âˆ´ Â Â Â Â Â Â Â

Maximum height:

Maximum height is the greatest height to which the projectile rises above point of projection. It is represented by H.

The displacement of projectile in vertical direction is given by,

Â Â Â Â Â Â Â Â Â Â Â

At the highest point, vertical component of velocity is zero.

âˆ´ Â Â Â Â

Horizontal range:

It is the horizontal distance travelled by the projectile during it's flight. i.e., the horizontal distance travelled covered by object. It is represented by R.

Obviously, it is the distance travelled by projectile in horizontal direction with constant velocity u cosÎ¸ in interval equal to time of flight.

i.e. Â Â Â

Â Â Â Â

Â

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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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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.Â

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