Answer:
[tex]h = 5.505\,m[/tex]
Explanation:
Let assume that ball begins its movement at a height of zero. The height can be found by energy approach, to be precise, by Principle of Energy Conservation:
[tex]\frac{1}{2}\cdot (0.145\,kg)\cdot (12\,\frac{m}{s} )^{2}= \frac{1}{2}\cdot (0.145\,kg)\cdot (6\,\frac{m}{s} )^{2}+(0.145\,kg)\cdot (9,81\,\frac{m}{s^{2}} )\cdot h[/tex]
[tex]h = 5.505\,m[/tex]