If a stone dropped from the top of a tower travels half of the height of the tower during last second of its fall, the time of fall is (in seconds)

When a stone is dropped from the top of a tower, it falls freely under gravity. Let's solve the problem step by step.

1. The height H of the tower is determined by the formula:

   H = (1/2) g t^2
    

   This is because a stone dropped from the top of a tower falls with initial velocity u = 0.

2. The distance covered by the stone in the last second is:

   (1/2) g (2t - 1)
    

   Since a stone dropped from the top of a tower travels half of the tower's height in the last second:

   (1/2) g (2t - 1) = (1/2) [(1/2) g t^2]
    

3. Solving this step-by-step, we get the quadratic equation:

   t^2 - 4t + 2 = 0
    

4. Using the quadratic formula, we find:

   t = 2 + √2 seconds (≈ 3.41 seconds)
    

Thus, the total time of fall is approximately 3.41 seconds.