A stones drops from the edge of the roof .it passes a window2.5m high in 0.1s.how far is the roof above the top of the window?
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an example of this.
To find the height of the roof above the top of the window, we can use the equation of motion for an object in freefall:
h = ut + (1/2)gt^2
Where:
h = height of the object (roof above the top of the window)
u = initial velocity (in this case, 0 as the stone is dropped)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken to pass the window (0.1s)
Since the stone passes a window 2.5m high in 0.1s, we can substitute these values into the equation:
2.5 = (0) + (1/2)(9.8)(0.1^2)
First, let's calculate (1/2)(9.8)(0.1^2):
(1/2)(9.8)(0.01) = 0.049
Now, we can rearrange the equation and solve for h:
h = 2.5 - 0.049
h = 2.451 m
Therefore, the roof is approximately 2.451 meters above the top of the window.
To find the height of the roof above the top of the window, we can use kinematic equations of motion.
Let's define the given information:
- The height of the window = 2.5 meters
- Time taken by the stone to pass the window = 0.1 seconds
We can use the equation for distance covered during free fall, assuming the initial velocity is zero:
h = (1/2) * g * t^2
Where:
h is the height or distance covered (in meters)
g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
t is the time taken (in seconds)
Now, let's calculate the distance covered by the stone while passing the window:
h = (1/2) * 9.8 * (0.1)^2
= 0.049 m
Thus, the stone has covered a height of 0.049 meters while passing the window.
To find the distance between the roof and the top of the window, we subtract the height of the window from the total distance covered:
Distance = 0.049 - 2.5
= -2.451 meters
The negative sign indicates that the roof is 2.451 meters below the level of the window.
So, the roof is approximately 2.451 meters above the top of the window.