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 θ. 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 P↔(x, y).

Let O be the origin.

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

Motion along horizontal direction is,

...(1)

Motion along vertical direction is,

...(2)

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

...(3)

The equation of inclined plane is,

...(4)

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 obtain

Therefore distance OP is,

So, the distance travelled by the projectile is OP.

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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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