A roofing tile falls from rest off the roof of a building. An observer from across the street notices that it takes 0.48 s for the tile to pass between two windowsills that are 3.0 m apart. How far is the sill of the upper window from the roof of the building?
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To find the distance between the sill of the upper window and the roof of the building, we can use the equations of motion, specifically the equation for the distance traveled by an object under constant acceleration.
First, let's list down the known quantities:
- Time taken for the tile to pass between the two windowsills, t = 0.48 s
- Distance between the two windowsills, s = 3.0 m
Since the tile falls vertically downward, we can assume it undergoes free fall acceleration due to gravity (9.8 m/s²) in the downward direction.
Now, let's use the equation of motion for displacement (s):
s = ut + (1/2)at²
Where:
- s is the displacement (unknown)
- u is the initial velocity (0 m/s since it falls from rest)
- t is the time taken (0.48 s)
- a is the acceleration due to gravity (-9.8 m/s², considering the downward direction)
We can rearrange the equation to solve for s:
s = (1/2)at²
Substituting the known values:
s = (1/2)(-9.8 m/s²)(0.48 s)²
s = -4.7 m
The negative sign in the result indicates that the displacement is in the downward direction.
Therefore, the sill of the upper window is approximately 4.7 meters above the roof of the building.