Question

A stone is drop from a top of a building .a) How does it take to fall 19.6m. b) How fast does it moves at a end of this fall. c) what is its acceleration after 1s and 2s.



​

Answer 1

Given:-

• Initial Velocity of Stone = 0m/s

• Acceleration due to gravity = +9.8m/s²

• Height of Stone = 19.6m

To Find:-

• How much time it takes to fall 19.6m.

• Final Velocity at the end of this fall.

• Accceleration after 1s and 2s.

Formulae used:-

• h = ut + ½ × g × t²

• v² - u² = 2gh

where,

• h = Height
• g = Acceleration
• u = Initial Velocity
• v = Final Velocity
• t = Time.

Now,

→ h = ut + ½ × a × t²

→ 19.6 = 0 × t + ½ × 9.8 × t²

→ 19.6 = ½ × 9.8 × t²

→ 19.6/9.8 = ½ × t²

→ 2 = ½ × t²

→ 4 = t²

→ √t² = √4

→ t = 2s

Hence, Time taken by stone to cover 19.6m is 2s.

Therefore,

→ v² - u² = 2 × a × s

→ v² - (0)² = 2 × 9.8 × 19.6

→ v² = 19.6 × 19.6

→ √v² = √(19.6)²

→ v = 19.6m/s

Hence, The Final Velocity of stone is 19.6m/s

→ The Acceleration after 1s and 2s will be Constant i.e, g = +9.8m/s²

Answer 2

Answer:

$\underline{ \sf \:Given \: } :$

• it take to fall 19.6m.

$\underline{ \sf \: To\: Find \: } :$

• How does it take to fall 19.6m

• How fast does it moves at a end of this fall.

$\underline{ \sf \: Solution \: } :$

Total time taken for stone to fall, :

$\boxed{\sf \: g = 9.8 \: {ms}^{2} }$

a) How does it take to fall 19.6m. :

$\sf \leadsto \: 19.6 = 0(t) + \frac{1}{2} (g) {n}^{2} \\ \\ \sf \leadsto \: {n}^{2} = \frac{ \cancel{19.6} \times 2}{ \cancel{9.8} }\\ \\ \sf \leadsto \: {n}^{2} = 2 \times 2 \\ \\ \sf \leadsto \: {n}^{2} = 4 \\ \\ \sf \leadsto \: n = \sqrt{4} \\ \\ \sf \leadsto \: n \: = 2$

Therefore, displacement in last, that is the 2nd second,u

____________________________________

b) How fast does it moves at a end of this fall.

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

Substitute all values :

$\sf \leadsto \: {v}^{2} = 0 + 2 \times 9.8 \times 19.6 \\ \\ \sf \leadsto \: {v}^{2} \: = 384.16 \\ \\ \sf \leadsto \: v \: = \sqrt{384.16} \\ \\ \\ \sf \leadsto \: v = 19.6 m/s^2$