Question

find the kinetic energy of a stone of mass 15kg released from a height if 100 m where it strikes the ground​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Mass of stone = 15kg

Height = 100m

Initial velocity = zero (i.e., free fall)

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find kinetic energy of stone when it strikes the ground.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➳ We can apply concept of Energy conservation to solve this question.

◈ WHY ?

➠ In case of free fall, only gravitational force acts on the body and we know that, Gravitational force is conservative force.

➠ Mechanical energy (sum of potential energy and kinetic energy) of system is conserved when body is moving under the action of conservative force.

Let's solve it :)

$:\implies\tt\:(PE)_i+(KE)_i=(PE)_f+(KE)_f$

$:\implies\tt\:mgH+0=0+(KE)_f$

$:\implies\tt\:(KE)_f=15\times10\times 100$

$:\implies\underline{\boxed{\bf{\gray{(KE)_f=15000\:J=15\:kJ}}}}$

❂ Another way to solve :D

• Find final velocity of ball at which ball touches the ground. (Use third equation of kinematics)
• Apply formula of kinetic energy. You will get the same answer. :)

Answer 2

Given ,

Initial velocity (v) = 0 m/s

Height (h) = 100 m

Mass (m) = 15 kg

We know that , the Newton's third equation of motion is given by

(v)² - (u)² = 2as

Thus ,

(v)² - (0)² = 2 × 10 × 100

(v)² = 2000 m/s

Now , the kinetic energy of a body is given by

Kinetic energy (KE) = 1/2 × m × (v)²

Thus ,

KE = 1/2 × 15 × 2000

KE = 15000 J or 15 Kilo joule

$\therefore$ The kinetic energy of stone is 15 KJ