A particle is projected from the surface of earth with intial speed of 4 km/s. Find the maximum height attained by the particle. Radius of earth = 6400 km and `g = 9.8 m//s^(2)`

Explanation

To find the maximum height attained by the particle projected from the surface of the Earth, we can use the principles of energy conservation. Here’s a step-by-step solution:

### Step 1: Understand the problem
We need to find the maximum height \( h \) attained by a particle projected with an initial speed \( v_0 = 4 \, \text{km/s} \) from the surface of the Earth. The radius of the Earth \( R = 6400 \, \text{km} \) and the acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \).

### Step 2: Convert units
Convert the initial speed and the radius of the Earth into meters for consistency:
- \( v_0 = 4 \, \text{km/s} = 4000 \, \text{m/s} \)
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