A particle is released from a height S . At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively

Step-by-step solution

We can realize the situation as shown. Let at point C distance x from highest point A , the particle's kinetic energy is three times its potential energy. Velocity C , v 2 = 0 + 2 g x O r v 2 = 2 g x .....(i) Potential energy at , C = m g S - x … . . ( i i ) At Point C, Kinetic energy = 3 × potential energy ie, 1 2 m × 2 g x = 3 × m g ( S - x ) or x = 3 S - 3 x or 4 x = 3 S or S = 4 3 x or x = 3 4 S Therefore, from Eq.(i) v 2 = 2 g × 3 4 S Or v 2 = 3 2 g S o r v = 3 2 g S Height of the particle from the ground = S