A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3 h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity u → 0 = u 0 x ∧ and falls on the ground at a distance d from the building making

Step-by-step solution

Using energy conservation, m g h = 1 2 m u 0 2 ⇒ u 0 = 2 g h u 0 is the horizontal component of the velocity throughout the flight. For vertical component of the velocity(just before collision with the ground), we can use equation of motion v z 2 = 0 2 + 2 - g - 3 h ⇒ v z = 6 g h Angle θ can be written as, tan θ = v z u = 3 ⇒ θ = 60 o Horizontal distance covered just before the collision will be, d = u 0 T = u 0 2 3 h g = 2 g h 2 3 h g = 2 3 h After collision, only velocity along z