An inclined plane makes an angle 30° with the horizontal and slopes downward in the direction of projection. A particle is projected horizontally from a point on the plane with speed 10√3 m/s. Neglect air resistance and take g = 10 m/s². The time after which the particle strikes the inclined plane again is:
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Question

An inclined plane makes an angle 30° with the horizontal and slopes downward in the direction of projection. A particle is projected horizontally from a point on the plane with speed 10√3 m/s. Neglect air resistance and take g = 10 m/s². The time after which the particle strikes the inclined plane again is:

Options

G1 Physics · Accepted Answer

Take the point of projection as origin, +x horizontal and +y vertically upward. For the projectile: x = (10√3)t and y = -(1/2)gt² = -5t². The downward inclined plane has equation y = -x tan30° = -x/√3. At impact: -5t² = -(10√3 t)/√3 = -10t. For t ≠ 0, 5t = 10, hence t = 2 s. Therefore option B is correct.