Question

A technician at the top of a 200m tall radio tower drops her hammer.
how much time does it take for the hammer to strike the ground?

Answer 1

ke at bottom = (1/2) m v^2 = m g h
so v at bottom = sqrt (2 g h)
so average v = max v/2 = (1/2) sqrt(2 gh)
average v = .5 sqrt(2*9.81*200)
= 31.3 m/s
time = distance /speed
= 200 /average v = 200/31.3 = 6.39 seconds

Answer 2

h=gt²/2
t=sqrt(2h/g) =sqrt(2•200/9.8)=6.39 s