Neglecting air resistance, a 1.0-kg projectile has an escape velocity of about 11km/s at the surface of Earth. The corresponding escape velocity for a 2.0 kg projectile is:

Options

A. 3.5 km/s
B. 5.5 km/s
C. 7.1 km/s
D. 11 km/s

Explanation

To determine the escape velocity for a 2.0 kg projectile, we need to understand that escape velocity is independent of the mass of the projectile. Here's how we can arrive at the solution step by step:

### Step-by-Step Solution:

1. **Understand Escape Velocity**: Escape velocity is the minimum velocity required for an object to break free from the gravitational attraction of a celestial body without any additional propulsion.

2. **Formula for Escape Velocity**: The escape velocity (V₀) can be derived from the energy conservation principle. The formula for escape velocity from the surface of a planet is given by:
\[ V_0 = \sqrt{\frac{2GM}{R}} \]
where G is the universal gravitational constant, M is the mass of the Earth, and R is the radius of the Earth.

3. **Given Information**: The problem states that a 1.0 kg projectile has an escape velocity of about 11 km/s. This value is derived from the formula above and is constant for any object projected from the surface of the Earth, regardless of its mass.

4. **Mass Independence**: Since escape velocity does not depend on the mass of the projectile, the escape velocity for a 2.0 kg projectile will be the same as that for a 1.0 kg projectile.

5. **Conclusion**: Therefore, the escape velocity for the 2.0 kg projectile is also:
\[ V_0 = 11 \text{ km/s} \]

### Final Answer:
The escape velocity for a 2.0 kg projectile is **11 km/s**.

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