Calculate Distance of Roof Above Window Top

[Kandy]

A roof tile falls from rest from the top of building. An observer inside the building notices that it takes 0.20 s for the tile to pass her window, whose height is 1.6 m. How far above the top of this window is the roof?

I attempted this question about 2 or 3 different ways but they don't work. I was wondering if it was 0.20s for the tile to go from the top of the window to the bottom of the window or from the roof to the bottom of the window, or something else. And the window having a height of 1.6m, does that mean from the top of the window to the bottom of the window it measures 1.6m? or from the gound to the bottom of the window, or from the ground to the top of the window?

 

[Fermat]

The height of the window is 1.6m. That's the distance from the top of it to the bottom of it.
The tile passes the window. It won't have passed the window unless it has passed all of it. So it must be 0.2s to pass by the botttom of the window, with the time starting from the top of the building.

 

[quicknote]

To accurately calculate the distance of the roof above the top of the window, we need to know the initial height of the roof and the final height of the window. From the given information, we can assume that the tile falls from the top of the roof to the bottom of the window, and the window has a height of 1.6m from the top to the bottom.

Using the formula h = 1/2gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time, we can calculate the height of the roof above the top of the window.

First, we need to find the time it takes for the tile to fall from the top of the roof to the bottom of the window. Since it takes 0.20 seconds for the tile to pass the window, we can assume that it takes the same amount of time for the tile to fall from the top of the roof to the bottom of the window.

Substituting the values into the formula, we get:

1.6m = 1/2 * 9.8m/s^2 * (0.20s)^2

Solving for the height of the roof, we get:

1.6m = 0.196m

Therefore, the roof is 0.196 meters above the top of the window. We can also convert this to centimeters, which is 19.6 cm.

In conclusion, the distance of the roof above the top of the window is 0.196 meters or 19.6 centimeters.