1.
[tex]Dane:\\m = 55 \ kg\\E_{p} = 22 \ kJ = 22 \ 000 \ J\\g = 10\frac{m}{s^{2}} = 10\frac{N}{kg}\\Szukane:\\h = ?\\\\Rozwiazanie\\\\E_{p} = mgh \ \ |:mg\\\\h = \frac{E_{p}}{mg}\\\\h = \frac{22000 \ J}{55 \ kg \cdot10\frac{N}{kg}} = \frac{22000 \ N\cdot m}{550 \ N}\\\\\boxed{h = 40 \ m}[/tex]
2.
[tex]Dane:\\m = 12 \ kg\\h = 10 \ m\\g = 10\frac{N}{kg}\\Szukane:\\E_{p} = ?\\\\Rozwiazanie\\\\E_{p} = mgh\\\\E_{p} = 12 \ kg\cdot10\frac{N}{kg}\cdot10 \ m\\\\\boxed{E_{p} = 1 \ 200 \ J = 1,2 \ kJ}\\\\(1 \ kJ = 1000 \ J)[/tex]
3.
[tex]Dane:\\m = 64 \ kg\\v = 20\frac{m}{s}\\Szukane:\\E_{k} = ?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2}\\\\E_{k} = \frac{64 \ kg\cdot(20\frac{m}{s})^{2}}{2}\\\\\boxed{E_{k} = 12 \ 800 \ J = 12,8 \ kJ}[/tex]
4.
[tex]Dane:\\v = 6\frac{m}{s}\\E_{k} = 9 \ kJ = 9 \ 000 \ J\\Szukane:\\m = ?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2} \ \ \ |\cdot\frac{2}{v^{2}}\\\\m = \frac{2E_{k}}{v^{2}}\\\\m = \frac{2\cdot9000 \ J}{(6\frac{m}{s})^{2}} = \frac{18000 \ kg\cdot\frac{m}{s^{2}}}{36\frac{m^{2}}{s^{2}}}\\\\\boxed{m = 500 \ kg}[/tex]
