The correct option is B 2+√2
Let h be the total distance covered in n second then,
for free fall h=12gn2
As per the question, distance covered by it in last second i.e. (n−1)th sec is given by
h′=h2=12gn22=14gn2
Thus, we have
12g(n−1)2=14gn2
Solving above equation we get a quadratic equation in n as
n2−4n+2=0
⇒ n=−(−4)±√(−4)2−4×22
⇒ n=4±2√22=2±√2
Now, n−1>0 if n=2−√2
⇒ (2−√2)−1>0⇒ 1−√2<0
Hence, the value of n is 2+√2.