Find the escape speed from the earth for a 6000kg spacecraft and find the kinetic energy it must have at the surface of the earth in order to escape the Earth's gravitational field? Mass of the earth is `5.98 xx 10^(24)kg` and its radius is `6.37 xx 10^(6) m`

Explanation

To solve the problem of finding the escape speed from the Earth for a 6000 kg spacecraft and the kinetic energy it must have at the surface of the Earth to escape the Earth's gravitational field, we can follow these steps:

### Step 1: Write down the given data
- Mass of the Earth (M) = \(5.98 \times 10^{24} \, \text{kg}\)
- Radius of the Earth (R) = \(6.37 \times 10^{6} \, \text{m}\)
- Mass of the spacecraft (m) = \(6000 \, \text{kg}\)
- Gravitational constant (G) = \(6.67 \times 10^{-11} \, \text{m}^3/\text{kg} \cdot \text{s}^2\)

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