38.Циолковский-2

$\tiny \vec{F}=M\vec{g}, Ox: M\frac{dV}{dt}=-Mg-U_{r}\frac{dM}{dt}\\ V=U_{r}ln\frac{M_{0}}{M}-gt, x=-\frac{gt^2}{2}+U_{r}\int_{0}^{t}ln\frac{M_{0}}{M(t))}dt \\ 1)M=M_{0}e^{-\alpha t}, \alpha=const => V=({\alpha U_{r}-g})t, x=({\alpha U_{r}-g})\frac{t^2}{2};\\ O|O_{x}=-U_{r}\frac{dM}{dt}=\alpha U_{r}M, \alpha U_{r}>g.\\ Characteristics: 1)t_{1}=\frac{1}{\alpha}ln\frac{M_{0}}{M_{k}}=\frac{n}{\alpha}, n=ln(1+\frac{M_{t}}{M_{k}})\\ 2)V_{1}=\frac{n}{\alpha}(\alpha U_{r}-g) 3)x1=(\alpha U_{r}-g)\frac{t_{1}^2}{2}=n^2\frac{\alpha U_{r}-g}{2\alpha^2}\\ h=\frac{V_{1}^2}{2g}=... => H=n^2(\frac{U_{r}^2}{2g}-\frac{U_r}{2\alpha})$