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Equation OF Trajectory || Maximum Range on Inclined Plane

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A particle is projected from the bottom of an inclined plane of inclination 30^@ . At what angle alpha (from the horizontal) should the particle be projected to get the maximum range on the inclined plane.

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A ring, disc, spherical shell and solid sphere of same mass and radius are rolling on a horizontal surface without slipping with same velocity. If they move up an inclined plane, which can reach to a maximum height on the inclined plane?

The ratio of the range of the particle and its maximum range in the inclined plane is:

STATEMENT-1: The maixmum range along the inclined plane, when thrown downward is greater than that when thrown upward along the same inclined plane with constant velocity. STATEMENT-2: The maximum range along inclined plane is independent of angle of inclination.

Find the equation of trajectory, time of flight , maximum height and horizontal range of a projectile when projected at an angle theta with the vertical direction .