[tex]Dane:\\a_1 = g\\a_2 = g-0,5g =0,5g\\Szukane:\\\frac{t_1}{t_2} = ?\\\\\\h = \frac{at^{2}}{2} \ \ /\cdot\frac{2}{a}\\\\t^{2}=\frac{2h}{a}\\\\t = \sqrt{\frac{2h}{a}}\\\\\\t_1 = \sqrt{\frac{2h}{a_1}} =\sqrt{\frac{2h}{g}}\\\\t_2 =\sqrt{\frac{2h}{a_2} } = \sqrt{\frac{2h}{0,5g}}\\\\\frac{t_2}{t_1} = \frac{\sqrt{\frac{2h}{0,5g}}}{\sqrt{\frac{2h}{g}}} =\sqrt{\frac{\frac{2h}{0,5g}}{\frac{2h}{g}}} = \sqrt{\frac{1}{0,5}} = \sqrt{2}\\\\t_2=\sqrt{2}t_1\\\\\boxed{t_2 \approx1,4t_1}[/tex]
Odp. Czas spadania zwiększy się ok.1,4 razy.
