Chapter 2.3, Problem 27P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to showthat differential equation $\frac{dr}{dt}=\frac{k}{\sqrt{r}}$ in explicitly deduce to that $r\left(t\right)\to \infty$ as $t\to \infty$ .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to deduce differential equation $\frac{dr}{dt}=\sqrt{\frac{k^2}{r}+\alpha }>\frac{h}{\sqrt{r}}$ , if the projectile is launched vertically with initial velocity $v_0>\sqrt{\frac{2GM}{R}}$ .