Question

A projectile is fired from the surface of earth of radius R with velocity KVe (where Ve is the escape velocity from surface of earth and K<1). Neglecting air resistance , what is the maximum height of rise from the center of earth?

Answer 1

k^2v^2 = 2gH

Answer 2

The solution must be in terms of K and R!

Answer 3

you are correct but it is not the answer i wanted

Answer 4

you have just applied the basic formula!

Answer 5

\[-\gamma\frac{Mm}{R}+\frac{1}{2}mk^2v_e^2=-\gamma\frac{M}{r}\]\[-\gamma\frac{M}{R}+\frac{1}{2}k^2v_e^2=-\gamma\frac{M}{r}\]\[\frac{1}{R}-\frac{k^2v_e^2}{2\gamma M}=\frac{1}{r}\quad,\quad\gamma M=gR^2\]\[\frac{1}{R}-\frac{k^2v_e^2}{2gR^2}=\frac{2gR-k^2v_e^2}{2gR^2}=\frac{1}{r}\]\[r=R\frac{2gR}{2gR-k^2v_e^2}\quad,\quad v_e^2=2gR\]\[r=\frac{R}{1-k^2}\]