A satellite is revolving round the earth in a circular orbit of radius `r` and velocity `upsilon_(0)`. A particle is projected from the satellite in forward direction with realative velocity `upsilon = (sqrt(5//4) - 1) upsilon_(0)`. Calculate its minimum and maximum distances from earth's centre during subsequent motion of the particle.

Explanation

To solve the problem, we need to calculate the minimum and maximum distances of a particle projected from a satellite revolving around the Earth. The satellite is in a circular orbit of radius \( r \) and velocity \( v_0 \). The particle is projected with a relative velocity of \( v = \left(\sqrt{\frac{5}{4}} - 1\right) v_0 \).

### Step-by-Step Solution:

1. **Determine the Orbital Velocity**:
The orbital velocity \( v_0 \) of a satellite in circular orbit is given by:
\[
v_0 = \sqrt{\frac{GM}{r}}
...