A stone is dropped from edge of a roof and is observed to pass a window, vertically below it. The stone takes 0.1 sec to fall between the top and bottom of the window. If the window is of 2 m height, how far is the roof above the top of the window?

h = V*t + 0.5g*t^2 = 2 m.

V*0.1 + 4.9*0.1^2 = 2.
0.1V = 2-0.049 = 1.95.
V = 19.5 m/s at top of the window.

V^2 = Vo^2 + 2g*h.
V = 19.5 m/s, Vo = 0, g = 9.8 m/s^2, h = ?.

To find the distance from the roof to the top of the window, we can use the equation of motion for an object in free fall:

s = u*t + (1/2)*g*t^2

where:
s = vertical distance traveled by the stone (unknown)
u = initial velocity of the stone (0 m/s since it's dropped)
t = time taken to fall between the top and bottom of the window (0.1 sec)
g = acceleration due to gravity (approximately 9.8 m/s^2)

We want to find the value of s. Rearranging the equation, we have:

s = (1/2)*g*t^2

Substituting the given values, we have:

s = (1/2)*(9.8 m/s^2)*(0.1 sec)^2

s = (1/2)*(9.8 m/s^2)*(0.01 sec^2)

s = 0.049 m

Therefore, the stone falls a distance of 0.049 m between the top and bottom of the window.

Since the window height is given as 2 m, we can now find the distance from the roof to the top of the window by subtracting the height of the window from the total distance fallen:

Distance from the roof to the top of the window = 0.049 m - 2 m

Distance from the roof to the top of the window = -1.951 m

However, since the distance cannot be negative, we can conclude that the roof is 1.951 m above the top of the window.

To find the distance between the roof and the top of the window, we can use the equation of motion for free fall:

h = 1/2 * g * t^2

Where:
h is the height or distance
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
t is the time it takes for the stone to fall

In this case, the stone takes 0.1 seconds (t = 0.1s) to fall from the top to the bottom of the window, which means it takes the same amount of time to fall from the roof to the top of the window.

Substituting the given values into the equation:

h = 1/2 * 9.8 m/s^2 * (0.1s)^2
h = 0.049 m

Therefore, the roof is approximately 0.049 meters (or 49 millimeters) above the top of the window.