The Total solution for NCERT class 6-12
A rocket is fired vertically with a speed of5 km s–1 from the earth’s surface. How far fromthe 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.
8 × 106 m from the centre ofthe Earth
Velocity of the rocket, v =5 km/s = 5 × 103 m/s
Height reached by rocket mass, m = h
At the surface of theEarth,
Total energy of the rocket= Kinetic energy + Potential energy
At highest point h,
Total energy of the rocket
From the law ofconservation of energy, we have
Total energy of the rocket at the Earth’ssurface = Total energy at height h
Height achieved by therocket with respect to the centre of the Earth