Question

A stone is dropped down a deep well from rest. the well is 50 metre deep how long will it take to reach the bottom of the wale? give a equals to 9.8 metre per second square​

Answer 1

$\bigstar$ Answer $\bigstar$

$\checkmark$ Given:

A stone is dropped down a deep well from rest

The well is 50 metre deep

$\checkmark$ To Find:

Time taken to reach the bottom of the well

$\checkmark$ Solution:

We know that,

$\star$ Equation of Motion

$\orange{\implies \sf s=ut+\dfrac{1}{2}gt^{2}}$

Here,

⇒ u = Initial Velocity

⇒ s = Height or Distance

⇒ g = acceleration due to gravity

⇒ t = time

According to the Question,

We are asked to find the Time taken to reach the bottom of the well

Therefore,

Given that,

s = 50 m

u = 0 m/s

g = 9.8 m/s²

Substituting the above values,

We get,

$\red{\implies \sf 50=(0)t+\dfrac{1}{2} \times 9.8 \times t^{2}}$

$\blue{\implies \sf 50=\dfrac{1}{2} \times 9.8 \times t^{2}}$

$\green{\implies \sf 50=4.9\times t^{2}}$

$\orange{\implies \sf t^{2}=\dfrac{50}{4..9} }$

$\red{\implies \sf t=\sqrt{\dfrac{50}{4.9}} \ sec}$

$\blue{\implies \sf t=\sqrt{10.20} \ sec}$

$\green{\implies \sf t=3.19 \ sec}$

$\pink{\implies \sf t \approx 3.2 \ sec}$

Therefore,

$\gray{\bold{\checkmark \ \sf { Time ( t ) = 3.2 \ sec}}}$

Hence,

Time taken to reach the bottom of the well is 3.2 seconds