Answer: h = 3R
Explanation:
Using the law of conservation of energy,
Total energy at the beginning of the launch would be equal to total energy at any point.
kinetic energy + gravitational potential energy = constant
Initial energy of the projectile =... (1)
where R is the radius of the Earth, M is the mass ofthe Earth, m is the mass of the projectile.
escape velocity,
Total energy at height h above the Earth where speed of the projectile is half the escape velocity:
...(2)
(1)=(2)
⇒
⇒
⇒
⇒
⇒h = 3R
Thus, at height equal to thrice radius of Earth, the speed of the projectile would reduce to half of escape velocity.