What will be the escape speed from a planet of mass `6xx10^(16)` kg and radius `3.6xx10^(4)` m ?

Explanation

To find the escape speed from a planet, we can use the formula:

\[ v = \sqrt{\frac{2GM}{R}} \]

where:
- \( v \) is the escape speed,
- \( G \) is the universal gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

### Step-by-Step Solution:

1. **Identify the values:**
- Mass of the planet, \( M = 6 \times 10^{16} \, \text{kg} \)
- Radius of the planet, \( R = 3.6 \times 10^{4} \, \text{m} \)
- Universal gravitational constant, \( G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)

2. **Substitute the values into the escape speed formula:**
\[ v = \sqrt{\frac{2 \times (6.67 \times 10^{-11}) \times (6 \times 10^{16})}{3.6 \times 10^{4}}} \]

3. **Calculate the numerator:**
- First, calculate \( 2 \times G \times M \):
\[ 2 \times (6.67 \times 10^{-11}) \times (6 \times 10^{16}) = 8.004 \times 10^{6} \]

4. **Calculate the denominator:**
- The radius \( R = 3.6 \times 10^{4} \)

5. **Divide the numerator by the denominator:**
\[ \frac{8.004 \times 10^{6}}{3.6 \times 10^{4}} = 222.33 \]

6. **Take the square root to find the escape speed:**
\[ v = \sqrt{222.33} \approx 14.91 \, \text{m/s} \]

### Final Answer:
The escape speed from the planet is approximately \( 14.91 \, \text{m/s} \).