Question

<13. A stone drops from edge of a roof it passe a window 2m high in 0.1 secod .
hw far is roof above the top of widow​

Answer 1

Answer:

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

Explanation:

Answer 2

Correct Question -

A stone is dropped from edge of a roof .It passes a window 2m high in 0.1 second. How far is roof above the top of window.

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Answer

(refer to the attachment)

Given -

s = 2m

t = 0.1 sec

a = g = 9.8

where

$\longrightarrow$s is distance travelled.

$\longrightarrow$t is time taken.

$\longrightarrow$a is acceleration due to gravity.

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To find -

Distance between roof and window$\longrightarrow$ h

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Formula used -

$\sf{v}^{2} = {u}^{2} + 2as$

$\sf{s = ut + \frac{1}{2} a {t}^{2}}$

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Solution -

Substituting the value in

$\sf{s = ut + \frac{1}{2} a {t}^{2}}$

$\implies$$\sf 2 = 0.1u + \frac{1}{2} \times 9.8 \times (0.1)^{2}$

$\implies$$\sf 2 = 0.1u + 4.9 \times 10 - 2$

$\implies$$\sf u = \frac{2 - 0049}{0.1} = 19.51 m/s$

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$\longrightarrow$u = 0 m/s ( stone is dropped )

$\longrightarrow$v = 19.51 m/s

$\longrightarrow$g = 9.8 m/s²

Substituting the value in

$\sf{v}^{2} = {u}^{2} + 2as$

$\implies$$\sf {{19.51}^{2} = 0 + 2 \times 9.8h}$

$\implies$$\sf h = \frac{ {19.51}^{2} }{19.6} = 19.42m$

Thus the roof is 19.42 m from the upper end of window.

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Thanks