A roof tile falls from rest from the top of a building. An observer inside the building notices that it takes 0.2s for the tile to pass her window, whose height is 1.6m. How far above the top of this window is the roof?

Answer 1

Let Y be the distance from roof to window top. Then Y + 1.6 is the distance from roof to window bottom.

Let T be the time to reach the top of the window. Then T + 0.2 is the time to reach the bottom of the window.

You have to solve two equations in two unknowns.

(g/2)T^2 = Y
(g/2)*(T+0.2)^2 = Y + 1.6

Y is the easiest to eliminate first. Subtract the first equation from the second and you get
1.6 m = 2*(g/2)(0.4T) + 0.04*(g/2)
Solve that for T.
Check my math; I tend to be sloppy. Once you have T, use the first equation to get Y.

Answer 2

you are sloppy. eaplain how y is easily eliminated please