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A projectile is projected with velocity  kve in vertically upward direction from the ground into the space. (ve  is escape velocity and  k < 1). If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)

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By Expert Faculty of Sri Chaitanya
a
Rk2+1
b
Rk2−1
c
R1−k2
d
Rk+1
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detailed solution

Correct option is C

Kinetic energy = Potential energy12mkve2=mgh1+hR⇒12mk22gR=mgh1+hR⇒h=Rk21−k2Height of Projectile from the earth's surface = hHeight from the centre  r=R+h=R+Rk21−k2By solving  r=R1−k2

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