Question

Sam throws a stone of mass 0.5 kg in the upward direction from the ground with a velocity of 10 ms${}^{-1}$. Calculate the kinetic energy and mechanical energy of the stone when it reaches (4/5)th of its maximum height.
Take g = 10 ms${}^{-2}$.

Answer 1

Given : Mass of stone = 0.5 kg, initial velocity of stone = 10 ms${}^{-1}$, g = 10 ms${}^{-2}$

To calculate maximum height of the stone,
Use 3rd equation of motion,
v${}^2$ - u${}^2$ = 2gh ..........(Taking upward direction as positive)
0 - (10)${}^2$ = 2 x (-10) x h
=> h = 5 m

Now, Mechanical Energy at h = 5 m will be equal to the potential energy at h = 5 m (Since KE will become 0)
Thus, Mechanical Energy at top = Potential Energy at top = mgh = 0.5 x 10 x 5 = 25 J

Mechanical Energy at h = (4/5)th of max height will also be 25 J (Since mechanical energy remains conserved)

Now, KE at height (4/5)th of max height = ME - PE = 25 - {0.5 x 10 x (4/5) x 5} = 25 - 20 = 5 J