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Kal ingenious from height of a certain height is kinetic energy street dance is potential energy

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Mohak Mansharamani asked in Science

fing the height at which kinetic energy is 1/4 of the potential energy , when a mass is dropped from a height of 20m. also find the velocity of mass at that point.

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Hansraj answered this
3509 helpful votes in Science, Class XII-Science

h = 20 m

Total mechanical energy at the height h = 20 m is,

E = mgh 

Let at height above the surface of the earth h' kinetic energy is 1/4 of the potential energy at his height.

K.E = 1/4(P.E)

1/2mv2 = 1/4(mgh') ....(i)

So at this height, total mechanical energy is ,

K.E + P.E = mgh

from (i),

1/4(mgh') + mgh' = mgh 

 1/4(h') + h' = 20

h' = 16 m

Substitute this  value in equation (i), take g = 10 m/s2 

We can calculate the velocity of the mass.