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do you want solution or concept
concept
i will tell you concept
you know kinetic energy changes to quater means its velocity change to 1/2 of intial
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on droping ftom H height on reaching ground its speed will be [2gH]^1/2
what time ball take to come at rest
i telling you concept if you need ans i will tell you
4[2g/H]^1/2
\(\color{red}{mgH} \to \dfrac{1}{2} m v^2\to \dfrac{1}{4}*\dfrac{1}{2} m v^2\to \color{red}{\dfrac{mgH}{4}} \) \(H \to \dfrac{H}{4} \to \dfrac{H}{16}\) @osprey is right on this. classically, it will never come to rest.
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