# 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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