Question

a stone dropped from edge of roof it passes a window to 2 m high in 0.1 seconds how far is the roof above the top of window

Answer 1

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