An earth satellite is revolving in a circular orbit of radius a with velocity `upsilon_(0)`. A gun is the satellite and is aimed directly towards the earth. A bullet is fired from the gun with muzzle velocity `(upsilon_(0))/(2)`. Neglecting resistance offered by cossmic dust and recoil of gun, calculate maximum and minimum distance of bullet from the centre of earth during its subsequency motion.

Explanation

To solve the problem, we need to find the maximum and minimum distances of the bullet from the center of the Earth after it is fired from the satellite. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Initial Conditions
- The satellite is in a circular orbit around the Earth with radius \( a \) and velocity \( v_0 \).
- A bullet is fired from the satellite with a muzzle velocity of \( \frac{v_0}{2} \) directly towards the Earth.

### Step 2: Determine the Initial Velocity of the Bullet
- The bullet's initial velocity \( v_{\text{net}} \) can be calculated as the vector sum of the satellite's orbital velocity \( v_0 \) and the bullet's muzzle velocity \( \frac{v_0}{2} \).
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