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 particle strikes the inclined plane again after:
Options

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 particle strikes the inclined plane again after:

Options

G1 Physics · Accepted Answer

Take the point of projection as origin, +x horizontal in the direction of projection and +y upward. Projectile: x = 10√3 t and y = -5t². The downward inclined plane is y = -x tan30° = -x/√3. At re-impact, -5t² = -(10√3 t)/√3 = -10t. For t ≠ 0, 5t = 10 ⇒ t = 2 s. Therefore option B is correct.