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  4. When a body is projected vertically up, its PE is twice its KE, when it is at a height h above the ground. At what height will its KE be twice the KE ?

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Q. When a body is projected vertically up, its PE is twice its KE, when it is at a height $h$ above the ground. At what height will its KE be twice the KE ?

NTA AbhyasNTA Abhyas 2020

Solution:

Total energy, $E_{1}=PE+KE$
$=PE+\frac{1}{2}PE=\frac{3}{2}PE=\frac{3}{2}mgh$
$E_{2}=PE+KE=PE+2PE+3PE=3mgh$
As, $E_{2}=E_{1}\Rightarrow 3mgh'=\frac{3}{2}mgh\Rightarrow h'=\frac{h}{2}$