Motion in A Plane

Physics Part I

Physics

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A projectile is projected horizontally with velocity from the top of an inclined plane of inclination Î¸. How far from the point of projection will the projectile hit tht plane?

Consider a projectile, which is projected with velocity 'u' in horizontal direction from a point O on an inclined plane and hit the inclined plane at Pâ†”(x, y).

Â Â Â Â Â Â

Let O be the origin.Â

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

On resolving the components of velocity and acceleration in horizontal and vertical direction, we have

Â

Motion along horizontal direction is,Â

Â Â Â Â Â Â Â Â Â Â Â Â ...(1)Â

Motion along vertical direction is,Â

Â Â Â Â Â Â Â Â ...(2)Â

Eliminating 't' from (1) and (2),Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(3)Â

The equation of inclined plane is,Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ...(4)Â

The point P is the intersection of trajectory and inclined plane, thus the coordinates of P are the solutions of equation (3) and (4).

By solving (3) and (4), we obtainÂ

Â Â Â Â Â

Therefore distance OP is,Â

Â Â Â Â Â Â Â

Â Â Â Â Â Â

So, the distance travelled by the projectile is OP.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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