Question

A stone is dropped from the height of 80 meters calculate time taken by the stone to reach the ground and calculate the speed of the stone just before touching the ground​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Distance (s) = 80 m

✭ Initial velocity (u) = 0 m/s

✭ Acceleration = Acceleration due to gravity (g) = 9.8 m/s²

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Final Velocity of the body?

◈ Time taken to reach the ground

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we may find the velocity of the body with the help of the third Equation of motion,

$\displaystyle\sf \underline{\boxed{\sf v^2-u^2=2as }}$

Later on we may find the time taken with the help of the first equation of motion, that is,

$\displaystyle\sf \underline{\boxed{\sf v = u+at}}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

By the third equation of motion,

$\displaystyle\sf \underline{\boxed{\sf v^2-u^2=2as }}$

Substituting the values,

$\displaystyle\sf \twoheadrightarrow v^2 = 2 \times 9.8 \times 80$

$\displaystyle\sf \twoheadrightarrow v^2 = 1568$

$\displaystyle\twoheadrightarrow\sf\orange{v = 39.6 \ m/s}$

Now by the first equation of motion,

$\displaystyle\underline{\boxed{\sf v = u+at}}$

Substituting the values,

$\displaystyle\sf\dashrightarrow v = u+at$

$\displaystyle\sf\dashrightarrow 39.6 = 9.8t$

$\displaystyle\dashrightarrow\sf\pink{t = 4 \ s}$

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