a stone drops from the edge of the roof. it crosses a window 2m long in 0.1sec. how much time does the stone take to reach the lower end of window from roof?

Answer 1

average speed crossing window = 20 m/s

now look at increase of speed in 2 meter drop
v = Vi + 9.8 (2)
call g = 10 for simplicity
v = Vi + 20
but we know (v+Vi)/2 = 20 the average
v = Vi + 20
v = -Vi + 40
0 = 2 Vi -20
Vi = 10 at top of window
so how long did it fall to the top of the window?
v = g t = 10
t = 1 second from roof to top of window
so time to bottom of window = 1 + .1 = 1.1 seconds

Answer 2

average speed crossing window = 20 m/s

now look at increase of speed in 2 meter drop
v = Vi + 9.8 (.1)
call g = 10 for simplicity
v = Vi + 1
but we know (v+Vi)/2 = 20 the average
v = Vi + 1
v = -Vi + 40
--------------
0 = 2 Vi -39
Vi = about 20 at top of window
so how long did it fall to the top of the window?
v = g t = 20
t = 2 second from roof to top of window
so time to bottom of window = 2 + .1 = 2.1 seconds