If a body is projected with speed `v` greater than escape speed `v_(e)` from the surface of earth, find its speed in intersteller space.

Explanation

To find the speed of a body in interstellar space when it is projected with a speed \( v \) greater than the escape speed \( v_e \) from the surface of the Earth, we can use the principle of conservation of mechanical energy. Here’s a step-by-step solution:

### Step 1: Understand the Concepts
The escape speed \( v_e \) is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. If a body is projected with a speed greater than \( v_e \), it will have some kinetic energy left when it reaches infinity.

### Step 2: Write the Energy Conservation Equation
According to the conservation of mechanical energy, the total mechanical energy at the surface of the Earth (initial point) must equal the total mechanical energy at infinity (final point). The equation can be expressed as:

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