Question

A projectile is fired vertically upwards from the surface of the earth with a velocity kv_e, where v_e is the escape velocity and k < 1. If R is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth will be : (Neglect air resistance)

• A.
• B.
• C. R (1 – k²)
• D.

Answer 1

Answer: (B)

Answer 2

If a body is projected from the surface of the earth with a velocity v and reaches a height h, then according to law of conservation of energy.

$\frac { 1 } { 2 }$ mv² =

Here v = kv_e = k

$\frac { 1 } { 2 }$ m k² . 2gR =

k²R $\left[ 1 + \frac { \mathrm { r } - \mathrm { R } } { \mathrm { R } } \right]$ = r – R

k²r = r – R or r = $\frac { \mathrm { R } } { 1 - \mathrm { k } ^ { 2 } }$