Question

A rocket is fired vertically with a speed of 5 km s^–1 from the earth’s surface. How far from the earth does the rocket go before returning to the earth? Mass of the earth = 6.0 × 10²⁴ kg; mean radius of the earth = 6.4 × 10⁶ m; G= 6.67 × 10^–11 N m² kg^–2.

Answer 1

Answer: 8 × 10⁶ m from the centre of the Earth

Velocity of the rocket, v = 5 km/s = 5 × 10³ m/s

Mass of the Earth,

Radius of the Earth,

Height reached by rocket mass, m = h

At the surface of the Earth,

Total energy of the rocket = Kinetic energy + Potential energy

At highest point h,

Total energy of the rocket

From the law of conservation of energy, we have

Total energy of the rocket at the Earth’s surface = Total energy at height h

Height achieved by the rocket with respect to the centre of the Earth