The hammer would be 4 storeys down.
The distance traveled by a freely falling body is given by the expression,
[tex] h= \frac{1}{2}gt^2 [/tex]
here, g is the acceleration due to gravity and t is the time taken.
The distance the hammer falls in 1 second is given by,
[tex] h= \frac{1}{2}gt^2 =\frac{1}{2}g(1 s)^2 =\frac{1}{2}g [/tex]
This is equal to the height of 1 storey.
If 1 more second elapses, the hammer is in air for 2 s.
The distance it falls in 2 seconds is given by,
[tex] h_1= \frac{1}{2}gt^2 =\frac{1}{2}g(2 s)^2 =4(\frac{1}{2}g) [/tex]
Since the height of 1 storey is given by,
[tex] h = \frac{1}{2}g [/tex]
Therefore,
[tex] h_1=4(\frac{1}{2}g) =4h [/tex]
The hammer would be 4 storeys down. It travels 1 storey in the 1st second and 3 storeys in the 2nd second.
