Question

A roof tile falls from rest from the top of a building. An observer inside the building notices that it takes 0.20s for the tile to pass her window, which has a height of 1.8cm. How far above the top of this window is the roof

Answer 1

Answer on question #63654, Physics / Mechanics — Relativity

Question A roof tile falls from rest from the top of a building. An observer inside the building notices that it takes 0.20s for the tile to pass her window, which has a height of 1.8m. How far above the top of this window is the roof

Solution Equation for moving along window is:

$\Delta s=v\Delta t+g\Delta t^{2}/2$

where $v$ is speed when start passing the window. From it we find

$v=\frac{\Delta s-g\Delta t^{2}/2}{0.2}=\frac{1.8-9.8\cdot 0.2^{2}/2}{0.2}=8.019\,m/s$

Knowing this speed we can find how far above the top of this window is the roof

$v=\sqrt{2gh}$

$h=\frac{v^{2}}{2g}=\frac{8.019^{2}}{2\cdot 9.8}\approx 3.28\,m$