A ball is dropped from a height H from rest. The ball travels H 2 in last 1 . 0   s . The total time taken by the ball to hit the ground is

Step-by-step solution

Given: Height of free fall of ball is H Distance covered by the ball is H 2 in last 1 . 0   s . Now, displacement in the n t h second s n = u + a n - 1 2 Here s n = H 2 , u = 0 (since the ball is at rest initially) Thus, H 2 = g n - 1 2             . . . 1 where n is the time taken to reach the ground n = 2 H g n 2 g 2 = H Substituting the value of n in equation 1 n 2 g 2 × 2 = g n - 1 2 n 2 = 4 n - 2 n 2 - 4 n + 2 = 0 n = 2 ± 2 n should be greater than 1 so, n = 2 + 2 =