A stone is dropped from the edge of the roof .It passes a window 2m high in 0.1s.How far is the roof above the window?
Answers
The object is falling under gravity. As it is moving towards the earth, Its acceleration is +g.
As it is dropped, It has initial velocity = 0 .
The stone passes the window of 2m high in 0.1s .
Let the distance between the roof and that window be " k " k
m and the time taken to reach that " k "m is t
That is k = 1/2gt² ( From the second equation of motion)
Given that, Stone passes through the window in 0.1 second.
So it travels k+2 m in t + 0.1seconds .
k + 2 = 1/2g(t+ 0.1)²
Substituting the value of k,
1/2gt² + 2 = 1/2g(t²+0.01 + 0.2t)
1/2gt² - 1/2gt² + 2 = 0.005 g + 0.1gt
2 = 0.005 * 10 + 0.1(10)t
2= 0.05 + t
2 - 0.05 = t
1.95 = t.
Therefore, The stone takes 1.95seconds to travel from roof to top of the window.
Now, We have to find The distance between roof and top of the window ( k)
k = 1/2(10)(t²)
k = 5t²
k = 5(1.95)²
k = 19.0125
Therefore, The height of the roof above the top of the window is 19.0125m
HOPE IT HELPS YOU !!