Themed Challenge (Frozen): The Evergrowing Olaf

Queen Elsa has just discovered a power she never knew she possessed. She has the ability to make Olaf much taller! Her powers can make Olaf grow continuously at a rate of \(10\) \(cm./s\). To test how fast Olaf grows, Elsa will throw a snowball up at the speed of \(x\) \(m/s\), in such a way that as Olaf grows, he should catch the snowball at its apex, before its descent. Olaf, being a snowman, can only grab things up to just below his height. If Olaf is originally \(0.5\) meters tall, and acceleration due to gravity is \(9.8\) \(m/s^{2}\), what is the maximum integer value of \(x\) such that Olaf can catch the snowball?

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