1.
[tex]dane:\\m = 3 \ t = 3 \ 000 \ kg\\h = 30 \ m\\t = 20 \ s\\g = 10\frac{N}{kg}\\szukane:\\a) \ W = ?\\b) \ P = ?\\\\Rozwiazanie\\\\a)\\W = E_{p} = mgh\\\\W = mgh\\\\W = 3000 \ kg\cdot10\frac{N}{kg}\cdot30 \ m\\\\W = 900 \ 000 \ J = 900 \ kJ\\\\b)\\P = \frac{W}{t}\\\\P = \frac{900000 \ J}{20 \ s}\\\\P = 45 \ 000 \ W = 45 \ kW[/tex]
2.
[tex]dane:\\m = 0,3 \ kg\\E_{k} = 9 \ 000 \ J\\szukane:\\v = ?\\\\Rozwiazanie\\\\E_{k} = \frac{mv^{2}}{2} \ \ /\cdot\frac{2}{m}\\\\v^{2} = \frac{2E_{k}}{m}\\\\v = \sqrt{\frac{2E_{k}}{m}} = \sqrt{\frac{2\cdot9000 \ J}{0,3 \ kg}} = \sqrt{\frac{18000 \ kg\cdot\frac{m^{2}}{s^{2}}}{0,3 \ kg}}=\sqrt{60000\frac{m^{2}}{s^{2}}}\\\\v\approx244,95\frac{m}{s}[/tex]
3.
[tex]dane:\\m = 3 \ kg\\h = 45 \ m\\g = 10\frac{N}{kg}\\szukane:\\E_{p} = ?\\\\Rozwiazanie\\\\E_{p} = m\cdot g\cdot h\\\\E_{p} = 3 \ kg\cdot10\frac{N}{kg}\cdot45 \ m\\\\E_{p} = 1 \ 350 \ J = 1,35 \ kJ[/tex]
