Question

The maximum vertical distance through which a full dressed astronaut can jump on the earth is 0.5 m . Estimated the maximum vertical distance through which he can jump on yhe moon which has a mean density 2/3rd that of the earth and radius one quater that of the earth

Answer 1

Dear student
$$\begin{gathered} maximheighth=0.5m \\ onearthastrunotsworksonpres\sin gitandgainsKEwhichissameonbothearthandmoon \\ soonbothplanetsinitialvelocityrecievedissame \\ onearth{v}^2-u^2=2gh \\ givesh=u^2/2g_e=0.5masg=G\rho \frac{4\pi R}{3} \\ onmoong=G\frac{\rho *2*(4/3\pi (R/4{)}^3)}{3*(R/4{)}^2}=g/6 \\ heightachievedonmoon=h\text{'}=u^2/2g_m=\frac{u^2}{2g/6}=6h=6*0.5=3m \end{gathered}$$