To determine the distance above the top of the window where the roof tile fell from, we can use the equations of motion. Let's break down the problem and solve it step by step:
1. First, we need to find the time it takes for the roof tile to fall from the top of the building to the height of the window. We can use the equation of motion:
h = 0.5 * g * t^2
where,
h is the height of the window (1.18 m),
g is the acceleration due to gravity (9.8 m/s^2),
t is the time taken to pass the window (0.10 s).
Rearranging the equation to solve for time, we get:
t = sqrt(2h / g)
Substituting the given values, we have:
t = sqrt(2 * 1.18 / 9.8)
≈ 0.1542 s
So, it takes approximately 0.1542 seconds for the roof tile to fall to the height of the window.
2. Now, to find the distance above the top of the window where the roof tile fell from, we can use the equation of motion again:
h = v0 * t + 0.5 * g * t^2
where,
v0 is the initial velocity of the tile (which is zero since it falls from rest),
t is the time it takes to pass the window (0.10 s),
h is the height of the window (1.18 m).
Simplifying the equation, we have:
h = 0 + 0.5 * g * t^2
Rearranging the equation to solve for h, we get:
h = 0.5 * g * t^2
Substituting the given values, we have:
h = 0.5 * 9.8 * 0.1542^2
≈ 0.1145 m
Therefore, the roof tile fell from a distance approximately 0.1145 meters above the top of the window.