Answer to Question #201856 in Astronomy | Astrophysics for Wen Lin

Question

A projectile is launched into space with a given initial velocity. How can calculate its maximum height? Acceleration is not constant (must use Newton's law of gravitation)

Mass is not given

Answer 1

$$\frac{1}{2}mv^2-\frac{GmM}{R}=-\frac{GmM}{R+h}\\ \frac{1}{2}v^2-\frac{GM}{R}=-\frac{GM}{R+h}$$