Question
Question: A stone is allowed to fall from the top of a tower and cover half the height of the tower in the las...
A stone is allowed to fall from the top of a tower and cover half the height of the tower in the last second of its journey. The time taken by the stone to reach the foot of the tower is
A
(2 - √2)s
B
4 s
C
(2 + √2)s
D
(2 ± √2)s
Answer
(2 ± √2)s
Explanation
Solution
Using h/2 = g/2 (2n - 1) and h = 1/2 gn2
(where n = total time and last moment of motion is nth second).
We get n2 – 4n + 2 = 0
Solving, n = (2 ± √2)s