A space-ship is launched into a circular orbit close to the Earth,s surface. What additional speed should now be imparted to the spaceship so that it overcome the gravitational pull of the Earth.
Take kinetic energy of the space-ship,
K = total energy of space-ship `= (GMm)/(2R)`
where m = mass of space-ship, M= mass of the earth and R = radius of the earth.

Explanation

To find the additional speed that should be imparted to a spaceship in a circular orbit close to the Earth's surface so that it can overcome the gravitational pull of the Earth, we can follow these steps:

### Step 1: Understand the Kinetic Energy in Orbit
The kinetic energy (K) of the spaceship in a circular orbit close to the Earth's surface is given by:
\[ K = -\frac{GMm}{2R} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
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