A roofing tile falls from rest off the roof of a building. An observer from across the street notices that it takes 0.42 s for the tile to pass between two windowsills that are 3.08 m apart. How far is the sill of the upper window from the roof of the building?
To solve this problem, we can use the equation of motion for objects in free fall. The equation is as follows:
d = vit + 0.5at^2
Where:
- d is the distance covered by the object
- vi is the initial velocity of the object (in this case, the tile is at rest, so vi is 0)
- t is the time it takes for the tile to pass between the two windowsills
- a is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, we want to find the distance from the sill of the upper window to the roof. So, we can rewrite the equation as:
d = 0 + 0.5at^2
Now, we need to calculate the time it takes for the tile to pass between the two windowsills. According to the problem, this time is 0.42 seconds.
Substituting the given values into the equation, we have:
d = 0.5 * 9.8 * (0.42)^2
d = 0.5 * 9.8 * 0.1764
d = 0.5 * 1.73112
d ≈ 0.8656 meters
Therefore, the distance from the sill of the upper window to the roof of the building is approximately 0.8656 meters.
To find the distance between the sill of the upper window and the roof of the building, we can use the formula for the distance covered during constant acceleration:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the tile falls freely under the influence of gravity, so the acceleration is equal to the acceleration due to gravity (g ≈ 9.8 m/s^2).
However, since the tile falls from rest, the initial velocity is 0 m/s, so the equation simplifies to:
distance = (1/2) * acceleration * time^2
Now, we can plug in the given values:
distance = (1/2) * 9.8 m/s^2 * (0.42 s)^2
distance = 0.5 * 9.8 m/s^2 * 0.1764 s^2
distance = 0.5 * 9.8 m/s^2 * 0.1764 s^2
distance ≈ 0.86 meters
Therefore, the sill of the upper window is approximately 0.86 meters from the roof of the building.