A particle is released from a height S. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
Text Solution
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We can realize the situation as shown. Let at point C distance x from highest point A, the particle's kinetic
energy is three times its potential energy.
Velocity C,
v 2 = 0 + 2gx
Or v 2 = 2gx.....(i)
Potential energy at, C = mg (S - x) .....(ii)
At Point C,
Kinetic energy = 3 x potential energy
i.e., 
m x 2gx = 3 x mg (S - x)
or x = 3S - 3x
or 4x = 35
or S= 
x
or 
Therefore, from Eq.(i)
Or 
or 
Height of the particle from the ground
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