Question

A rocket is launched straight up from the earth's surface at a speed of 14500 m/s. What is its speed when it is very far away from the earth?

Answer 1

We know that energy is conserved .

Now total energy at the surface of the earth = total energywhen it is far away from earth.

total energy at the surface of the earth =(1/2)mu²-    GMm/R

total energy when it is far away from earth =(1/2)mv²

Then (1/2)mu²-    GMm/R   =(1/2)mv²

            (1/2)u² - GM/R   =(1/2)v²

            v = ?[ u² - (2GM/R)]  ---------1

Here G = 6.67 *10^-11Nm²/kg²

        M = mass ofthe earth = 5.98 *10²⁴kg

         R =radius of the earth = 6400 km = 6400000 m

         u = speed ofthe rocket at the surface of the earth = 1.45