A ball is thrown vertically down from a height of 40 ~m from the ground with an initial velocity v . The ball hits the ground, loses 1 3 rd of its total mechanical energy and rebounds back to the same height. If the acceleration due to gravity is 10 ~ms ⁻² , then the value of v is

Step-by-step solution

As per question, the ball hits the ground loses 1 3 rd of its total mechanical energy and rebounds back to the same height. aligned & i.e., 2 3 ( 1 2 m v^2+m g h )=m g h & 2 3 ( 1 2 v^2+g h )=g h & v^2 3 =g h- 2 g h 3 & v^2 3 = g h 3 v= g h & v= 400 =20 ~m / s aligned