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

<p><span contenteditable="false"> <math> <mi mathvariant="normal">U</mi> <mo>+</mo> <mi mathvariant="normal">K</mi> <mi mathvariant="normal">E</mi> <mo>=</mo> <mi mathvariant="normal">E</mi> </math> </span></p><p><span contenteditable="false"> <math> <mn>4</mn> <mi mathvariant="normal">U</mi> <mo>=</mo> <mi mathvariant="normal">E</mi> <mo>=</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">S</mi> </math> </span></p><p><span contenteditable="false"> <math> <mn>4</mn> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">h</mi> <mo>=</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">S</mi> </math> </span></p><p><span contenteditable="false"> <math> <mi mathvariant="normal">h</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </mfrac> </math> </span></p><p><span contenteditable="false"> <math> <mi mathvariant="normal">v</mi> <mo>=</mo> <mroot> <mrow> <mrow> <mn>2</mn> <mtext> </mtext> <mi mathvariant="normal">g</mi> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mtext> </mtext> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mroot> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>3</mn> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">S</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span></p>

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