A ball is released from a height h . If t 1 and t 2 be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t 1 and t 2 .

Step-by-step solution

As the body is dropped from a certain height h , its initial velocity will be zero. For first half, h 1 = h 2 . Using second equation of motion, s = u t + 1 2 a t 2 We have, h 2 = 1 2 g t 1 2 . Time taken in travel first half of the height, t 1 = h g         . . . 1 . For total height h , using again second equation of motion, h = 1 2 g t 1 + t 2 2 ⇒ t 1 + t 2 = 2 h g         . . . 2 From equation 1 and 2 , ⇒ 1 2 = t 1 t 1 + t 2 ⇒ 1 + t 2 t 1 = 2 ⇒ t 1