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 x 1024 kg; mean radius of the earth = 6.4 x 106 m; G= 6.67 x 10-11 N m2 kg-2
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
