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Question

Sam throws a stone of mass 0.5 kg in the upward direction from the ground with a velocity of 10 ms1. Calculate the kinetic energy and mechanical energy of the stone when it reaches (4/5)th of its maximum height.
Take g = 10 ms2.

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Solution

Given : Mass of stone = 0.5 kg, initial velocity of stone = 10 ms1, g = 10 ms2

To calculate maximum height of the stone,
Use 3rd equation of motion,
v2 - u2 = 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

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