An earth satellite is revolving in a circular orbit of radius a with velocity `upsilon_(0)`. A gun in the satellite is aimed directly towards the earth. A bullet is fired from the gun with muzzle velocity `(upsilon_(0))/(2)`. Neglecting resistance offered by cosmic dust and recoil of gun, calculate maximum and minimum distance of bullet from the center of earth during its subsequent motion.

Answer

3

Explanation

`v_(0)=sqrt((GM)/a)`
`mv_(0)a=mvr`
`1/2m(v_(0)^(2)+(v_(0)^(2))/4)-(GMm)/a=1/2mv^(2)-(GMm)/r`
Solving `(r_(max))/(r_(min))=(2a)/(2a//3)=3`