maximum height reached by a bullet fired vertically upward with a speed equal to 50% if the escape velocity from earth's surface is (R is radius of earth):

Options

A. `R//3`
B. `R//2`
C. `16R//9`
D. `R//8`

Answer

A

Explanation

`1/2m(v_(e)/2)^(2)-(GM_(e)m)/R_(e) = 0-(GM_(e)m)/(R_(e)+h))`
`1/2m((2gR_(e))/4)-mgR_(e)=-(mgR_(e)^(2))/((R_(e)+h))`
`(mgR_(e))/4-mgR_(e)=-(mgR_(e)^(2))/(R_(e)+h)`
`-(3mgR_(e))/4=-(mgR_(e)^(2))/(R_(e)+h)`
`3R_(e)+3h=4R_(e)`
h=R_(e)//3`