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A falling stone takes 0.2 sec to fall past a window which is 1 m high.from how far above the top of the window was the stone dropped

 A falling stone takes 0.2 sec to fall past a window which is 1 m high.from how far above the top of the window was the stone dropped 

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
 Let V0 = the underlying speed of the stone as it crossed the top edge of the window 
Let h = the tallness over the window that the stone was dropped with no underlying speed. 
Let g = the speeding up because of gravity = 9.8 m/s² 
Let t = the time that it takes to fall past the window = 0.2 s 
Let d = the tallness of the window = 1 m 
Utilizing the separation condition for steady speeding up with an underlying speed: 
d = (V0)(t) + (1/2)(g)(t²) 
The underlying speed condition is: 
V0 = √{(2)(g)(h)} 
Substitute √{(2)(g)(h)} for V0: 
d = √{(2)(g)(h)}t + (1/2)(g)(t²) 
Unravel for h: 
√{(2)(g)(h)}t = d - (1/2)(g)(t²) 
(2)(g)(h)t² = {d - (1/2)(g)(t²)}² 
h = {d - (1/2)(g)(t²)}²/{2(g)(t²)} 
h ≈ 0.824 m 

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