A falling stone takes 0.28 s to travel past a window 2.2 m tall. From what height above the top of the window did the stone fall?
To find the height from which the stone fell, we need to use the equation of motion for free fall:
s = ut + (1/2)gt²
Where:
s is the total distance traveled (in this case, the height of the window),
u is the initial velocity (which starts from rest, so u = 0),
t is the time taken (0.28 s),
g is the acceleration due to gravity (approximately 9.8 m/s²).
Since the stone starts from rest, the velocity component (u) is equal to zero. The equation can be simplified to:
s = (1/2)gt²
We know that s is the height of the window, which is 2.2 m. Substituting the values into the equation:
2.2 = (1/2)(9.8)(0.28)²
Now let's solve the equation to find the height from which the stone fell:
First, square the given time:
0.28² = 0.0784
Next, multiply the result by half of the acceleration due to gravity:
(1/2)(9.8)(0.0784) = 0.386144
Finally, divide the height of the window by the result to find the height from which the stone fell:
2.2 / 0.386144 ≈ 5.70
Therefore, the stone fell from a height of approximately 5.70 meters above the top of the window.
To find the height from which the stone fell, we can use the equations of motion for freefall.
We have the following variables:
- Initial velocity (u) = 0 m/s (the stone is dropped, not thrown)
- Final velocity (v) = ? (final velocity when it hits the ground)
- Acceleration (a) = 9.8 m/s^2 (acceleration due to gravity)
- Time (t) = 0.28 s
- Distance (s) = 2.2 m (height of the window)
Using the equation: s = ut + (1/2)at^2, we can solve for the initial height (s):
s = ut + (1/2)at^2
2.2 m = 0 m/s * 0.28 s + (1/2) * 9.8 m/s^2 * (0.28 s)^2
Simplifying the equation:
2.2 m = 0 + (1/2) * 9.8 m/s^2 * 0.0784 s^2
2.2 m = 0 + 4.9 m/s^2 * 0.0784 s^2
2.2 m = 0.38416 m
Therefore, the stone fell from a height of approximately 0.38 m above the top of the window.