Question

answer the question!!!!!! ​

Answer 1

Given:-

• Initial velocity of Stone = 0m/s

• Height above the top of a window = 10m

• Height of window = 4.4

• Acceleration due to gravity = + 10m/s²

To Find:-

• The Time taken by the stone to cross the top to bottom of the window.

Formulae used:-

• s = ut + ½ × a × t²

Where,

• s = Distance
• u = Initial Velocity
• a = Acceleration

t = Time

Now,

Time taken to cross the height of 10m

→ s = ut + ½ × a × t²

→ 10 = 0 × t + ½ × 9.8 × t²

→ 10 = 4.9t²

→ t² = 10/4.9

→ t² = 2.04

→ t (x) = 1.42s

Hence, The time taken to cross the 10m height is 1.42s

Again,

→ Total Distance = 10 + 4.4

→ Total Distance = 14.4m

→ s = ut + ½ × a × t²

→ 14.4 = 0 × t + ½ × 9.8 × t²

→ 14.4 = 0 + 4.9t²

→ 14.4 = 4.9t²

→ t² = 14.4/4.9

→ √t² = √2.93

→ t ( y ) = 1.71s

Hence, The time taken by stone to cross whole height is 1.7s

Therefore,

→ Time taken to cross the top of window = y - x

→ 1.71 - 1.42

→ 0.29s

Therefore, The time taken by stone to

stone tocross from the top to bottom of the wwindo is 0.29s.

Answer 2

Question:-

• A stone is dropped from the height of 10m from the top of a window of height 4.4m. (top to the bottom). Find the time taken by the stone to cross from the top to the bottom of this window.

Given:-

• initial velocity (u) = 0m/s
• height above the window = 10m
• height of the window = 4.4m
• acceleration due to gravity (g) = 10m/s²

Note:- the actual value of g is 9.8m/s² but in order for easiness, we use 10m/s²

To find:-

• time taken by this stone to reach the bottom of this window

Formula to be used:-

$\underline{\boxed{\bf S = ut + \dfrac{1}{2} gt²}}$

here,

• S = distance (height)
• u = initial velocity
• t = time taken
• g = acceleration due to gravity

Solution:-

Time taken to cross 10m height

$\longrightarrow$ 10 = 0×t + $\sf\dfrac{1}{2}$ × 10 × t²

$\longrightarrow$ 10 = 5×t²

$\longrightarrow$ 2 = t²

$\longrightarrow$ t = √2

$\longrightarrow$ t = 1.4 sec.

hence, the time taken to reach 10m is 1.4 sec.

Time taken to cross the bottom of window:-

• Total distance = height above the window + height of the window

$\longrightarrow$ 10+4.4 = 14.4m

$\longrightarrow$ 14.4 = 0×t + $\sf\dfrac{1}{2}$ × 10 × t²

$\longrightarrow$ 14.4 = 5×t²

$\longrightarrow$ 2.88 = t²

$\longrightarrow$ t = √2.88

$\longrightarrow$ t = 1.69 ~ 1.7 sec.

hence, the time taken to cross the bottom of the window is 1.7 sec.

Time taken by the stone to travel from the top to the bottom of the window = 1.7-1.4 = 0.3 sec.

Additional information:-

When the body is coming towards the centre of earth:-

• 1st equation of motion:-

$\longrightarrow$ $\underline{\boxed{\bf v = u+gt }}$

here,

• v = final velocity
• u = initial velocity
• g = acceleration due to gravity
• t = time taken

• 3rd equation of motion:-

$\longrightarrow$ $\underline{\boxed{\bf v² = u²+gh }}$

here,

• v = final velocity
• u = initial velocity
• g = acceleration due to gravity
• h = height