A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed o…

Question

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

Accepted Answer

Correct answer: C. (c) Using the equation of motion for velocity at height x : V^2=0+2g (S-x ) Simplifies to: V^2=2g (S-x ) Potential Energy at height x : Potential Energy = mgx Relation between kinetic and potential energy: Given that the kinetic energy is three times the potential energy, mgx=3 12mV^2 Simplifying gives: gx= 32 2g (S-x ) gx=3g (S-x )4x=S Solving for x : x= S4 Finding the speed V at this instant: V= 2g(S- S4)= 2g 3S4= 3 gS2 Thus, the height from the surface of the Earth is S4 and the speed of the particle at that height is 3 gS2.

$A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.$

Solution

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