A block is mass `m` is dropped from the fourth of an office building and hits the sidewalk below at speed `v` . From what floor should the block the dropped to double that impact speed?

Options

A. the either floor
B. the thenth floor
C. the twelfth floor
D. the sixteenth floor

Answer

D

Explanation

As the back falls freely, only the conservative gravitation force acts on it. Therefore, mechainical energy is conservate, or `KE_(f) = KE_(f) + PE_( C)` Assuming that the block is releasedfrom rest `(KE_(i) = 0)` and taking `y = 0` at ground level `(PE_(f) = 0)` we have that
`KE_(f) = PE_(i)` or `(1)/(2) mv_(1)^(2)` = mgy and `y_(i) = (v_(f)^(2))/(2g)`
Thus, to double the final speed, it is necessary to increase the initial height by a factor of four.