A particle is projected horizontally with speed u from a point at height h above the foot O. An inclined plane through O makes angle α above the horizontal.If x is the horizontal coordinate of the point where the projectile strikes the plane, then x satisfies:
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Question

A particle is projected horizontally with speed u from a point at height h above the foot O. An inclined plane through O makes angle α above the horizontal.If x is the horizontal coordinate of the point where the projectile strikes the plane, then x satisfies:

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G1 Physics · Accepted Answer

Take O as origin and y vertically upward. The projectile starts from (0,h) with horizontal speed u. Its trajectory is y = h - gx²/(2u²). The inclined plane is y = x tanα. At intersection, h - gx²/(2u²) = x tanα. Therefore, gx²/(2u²) + x tanα - h = 0.