As depicted in the figure, a particle slides on a frictionless track that terminates in a straight horizontal section. If the particle begins slipping from point A, determine how far away from the track the particle will hit the ground.

Step-by-step solution

Let the initial height of the particle be h₁ = 1.0 m and the height of the horizontal section of the track be h₂ = 0.5 m . By the principle of conservation of mechanical energy, the velocity v of the particle at the end of the track is given by: mg h₁ = mg h₂ + 1 2 m v^2 v = 2g(h₁ - h₂) Substituting the given values: v = 2g(1.0 - 0.5) = g The particle leaves the track horizontally. The time t taken to fall to the ground from height h₂ is: t = 2 h₂ g = 2(0.5) g = 1 g The horizontal distance x traveled by the particl