A particle is fired vertically upward fom earth's surface and it goes up to a maximum height of 6400 km. find the initial speed of particle.

Explanation

To find the initial speed of a particle fired vertically upward from the Earth's surface that reaches a maximum height of 6400 km, we can use the principle of conservation of energy. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We need to find the initial speed (u) of a particle that is projected from the Earth's surface and reaches a maximum height (h_max) of 6400 km. This height is equal to the radius of the Earth (R).

### Step 2: Set Up the Energy Conservation Equation
According to the conservation of mechanical energy, the total mechanical energy at the surface (initial) will be equal to the total mechanical energy at the maximum height (final).

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