Question

A projectile is fired from the surface of earth of radius R with a velocity h v_e where v_e is the escape velocity and h<1. Neglecting air resistance, the orbital velocity of projectile is –

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Answer 2

Let velocity at surface = v_s = hv_e

Velocity at orbit = v₀

By COE, $\frac { 1 } { 2 } \mathrm { mv } _ { \mathrm { s } } ^ { 2 } + \left( - \frac { \mathrm { GMm } } { \mathrm { R } } \right) = \frac { 1 } { 2 } \mathrm { mv } _ { 0 } ^ { 2 } - \frac { \mathrm { GMm } } { \mathrm { r } }$ …(1)

By Newton's law, …(2)

Solving (1) and (2)

v₀ = v_e$\sqrt { 1 - \eta ^ { 2 } }$