a stone drops from the edge of a roof. it passes a window 2 mtr high in 0.01 sec . how far is the roof above the top of the window?

To find the distance between the roof and the top of the window, we can use the formula for calculating the distance traveled by an object under free fall:

Distance (d) = initial velocity (v) * time (t) + 0.5 * acceleration (a) * time squared (t^2)

In this case, the stone is simply dropping under free fall, so its initial velocity is 0 m/s (since it starts from rest), and the acceleration due to gravity (a) is approximately 9.8 m/s^2 (assuming the absence of air resistance).

Let's calculate the distance traveled by the stone as it passes the window:

Distance = Initial velocity * Time + 0.5 * Acceleration * Time^2
Distance = 0 * 0.01 + 0.5 * 9.8 * (0.01)^2
Distance = 0 + 0.5 * 9.8 * 0.0001
Distance = 0.5 * 0.00098
Distance = 0.00049 meters

Therefore, the distance between the roof and the top of the window is approximately 0.00049 meters or 0.49 millimeters.

To find how far the roof is above the top of the window, we can use the equation for free fall motion:

d = 0.5 * g * t^2

Where:
d = distance traveled
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
t = time of travel

In this case, we know:
d = 2 m (height of the window)
t = 0.01 sec (time it took to pass the window)

First, let's find the distance traveled by the stone from the roof to the top of the window:

d = 0.5 * g * t^2
d = 0.5 * 9.8 * (0.01)^2
d = 0.5 * 9.8 * 0.0001
d = 0.00049 m

Now, to find the distance from the roof to the top of the window, we subtract the distance traveled (0.00049 m) from the height of the window (2 m):

Distance from roof to top of the window = 2 m - 0.00049 m
Distance from roof to top of the window ≈ 1.99951 m

Therefore, the roof is approximately 1.99951 meters above the top of the window.

Height =2m

Time -2s
Acceleration due to gravity-9.8
From second equation of motion

The distance traveled in .01 second at time t is

4.9(t+0.01)^2 - 4.9t^2 = 4.9(.02t+.0001)

So, if it fell 2m in that time,

4.9(.02t+.0001) = 2.0
t = 20.4

So, it had been falling for 20.4 seconds when it reached the window. Now just figure how far it fell in that time.