A projectile is launched vertically from earth's surface with an inittial velocity of 10 km/s. Calculate the height it will reach above the earth's surface. Take,
Radius of earth = 6,400 km
`g = 9.8 m//s^(2)`

Explanation

To solve the problem of calculating the height a projectile will reach when launched vertically from the Earth's surface with an initial velocity of 10 km/s, we will apply the principle of conservation of energy. Here are the steps to arrive at the solution:

### Step 1: Understand the Problem
We have a projectile launched from the Earth's surface with an initial velocity \( v_0 = 10 \, \text{km/s} \) (which is \( 10,000 \, \text{m/s} \)). We need to find the maximum height \( h \) it reaches above the Earth's surface.

### Step 2: Use Conservation of Energy
The total mechanical energy at the surface of the Earth (initial) will be equal to the total mechanical energy at the maximum height (final). The mechanical energy consists of kinetic energy (KE) and gravitational potential energy (PE).

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