[tex]Dane:\\v_{o} = 0\\t = 0,5 \ s\\g = 10\frac{m}{s^{2}}\\Szukane:\\a) \ h = ?\\b) \ v = ?\\\\Rozwiazanie\\\\a)\\h = \frac{1}{2}gt^{2}\\\\h = \frac{1}{2}\cdot10\frac{m}{s^{2}}\cdot(0,5 \ s)^{2}\\\\\boxed{h = 1,25 \ m}[/tex]
[tex]b)\\E_{p} = E_{k}\\\\mgh = \frac{mv^{2}}{2} \ \ /:m\\\\\frac{v^{2}}{2} = gh \ \ /\cdot2\\\\v^{2} = 2gh\\\\v = \sqrt{2gh}\\\\v = \sqrt{2\cdot10\frac{m}{s^{2}}\cdot1,25 \ m} = \sqrt{25\frac{m^{2}}{s^{2}}}}\\\\\boxed{v = 5\frac{m}{s}}[/tex]
