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

Options

A. `R/5`
B. `R/3`
C. `R/2`
D. `R/4`

Answer

B

Explanation

According to the law of conservation of energy,
`("Total energy")_("surface") = ("Total energy")_("max height")`
`!(KE+PE)_("surface")=(KE+PE)_("max height")` ltbr? `!1/2mv^(2)+(-(GMm)/R)=0+(-(GMm)/(R+h))`
Given, `1/2V_(e)=1/2sqrt((2GM)/R)`
`!1/2m[1/4dot(2GM)/R]-(GMm)/R=-(GMm)/(R+h)`
`!1/4(GMm)/R-(GMm)/R=-(GMm)/(R+h)`
`!(1-4)/(4R)=1/(R+h)!3R+3h=4R`
`!h=R/3`
So, option (b) is the correct answer.