Question

prove that the kinetic energy of a freely falling object on reaching the
ground is nothing but the transformation of its initial potential energy.
​

Answer 1

We need to prove that the kinetic energy of a free falling body on reaching the ground is equal to the initial potential energy.

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Let the mass of the body be m,

(1)

Here, The height of the body = h

And the velocity is 0 m/s because it is at rest.

⇒ $\quad$ Potential Energy = mgh ...(1)

⇒ $\quad$ Kinetic Energy = 1/2 × m × 0²

⇒ $\quad$ Kinetic energy = 0 ...(2)

(2)

In this case, The body travels half of the total height.

∴ $\quad$ Height, = h/2

So,

⇒ $\quad$ Potential Energy = mg×h/2

⇒ $\quad$ Potential energy = mgh/2 ...(3)

Let the velocity of the body be v at this moment.

⇒ Kinetic energy = 1/2 × m × v²

Here, The body lost half of its potential energy [ from (3) ] , Hence, According to the law of conservation of energy, Kinetic energy = mgh/2

(3)

Here, The height is 0 m because the body has reached the ground.

⇒ $\quad$ Potential energy = m × g × 0

⇒ $\quad$ Potential energy = 0 ...(4)

And,

⇒ $\quad$ Kinetic energy = 1/2 mv² ...(5)

Here, The kinetic energy = mgh, because the body has lost all its potential energy, and According to the law of conservation of energy, Kinetic energy = mgh.

Hence, Proved.