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 x 10²⁴ kg; mean radius of the Earth = 6.4 x 10⁶ m; G = 6.67 x 10^-11 Nm²kg^-2

Answer 1

Initial kinetic energy of the rocket

= 1/2mv² = 1/2 x m x (5000)² - 1.25 x 10⁷mJ

At distance of 'r' from the centre of the earth, K.E. becomes zero

The change in K.E.

= 1.25 x 10⁷ - 0 = 1.25 x 10⁷ mJ

This energy changes into potential energy.