Stone’s Fall: Time and Speed Calculation

Question:

A stone is dropped from the top of a building of height 20 m.Find the time taken for the stone to reach the ground.Also find the speed of the stone just before hitting the ground.

Solution:

Time taken to reach the ground

Initial velocity of the stone (u) = 0

The displacement for the stone is s=-h=-20 m

For freely falling body $${h=\frac{1}{2}gt^2}$$

$${t=\sqrt \frac{2h}{g}}$$

$${t=\sqrt\frac{(2)(20)}{10}}$$

$$t=\sqrt 4$$

$$t=2 s$$

Time taken for the stone to reach the ground = 2 s

Speed of the stone just before hitting:

For freely falling body the velocity before hitting the ground is

$${v=\sqrt {2gh}}$$

$${v=\sqrt{2(10)(20)}}$$

$$v={\sqrt 400}$$

$$v=20 \frac{m}{s}$$

Speed of the stone just before hitting the ground = 20 ms^-1