An astronaut accidentally gets separated out his small spaceship accelerating in interstellar space at a constant rate of `100ms^(-2)` . What is the acceleration of the astronaut the instant after he is outside the spaceship? (Assume that there are no nearby stars to exert gravitational force on him)

Options

A. zero
B. `10ms^(-2)`
C. `50ms^(-2)`
D. `100ms^(-2)`

Explanation

To solve the problem, we need to analyze the situation step by step:

### Step 1: Understand the Initial Conditions
The astronaut is inside a spaceship that is accelerating at a constant rate of \(100 \, \text{m/s}^2\). While inside the spaceship, the astronaut experiences a force due to this acceleration, which can be thought of as a pseudo force acting on him.

**Hint:** Consider the effects of acceleration on the astronaut while he is still inside the spaceship.

### Step 2: Identify Forces Acting on the Astronaut
While the astronaut is inside the spaceship, he feels a normal force from the chair or seat he is sitting on, which balances the pseudo force due to the spaceship's acceleration. The net force acting on him while inside the spaceship is non-zero, resulting in an acceleration of \(100 \, \text{m/s}^2\).

**Hint:** Recall that the net force is what causes acceleration according to Newton's second law.

### Step 3: Analyze the Situation After Separation
Once the astronaut accidentally separates from the spaceship, he is no longer in contact with it. In interstellar space, we assume there are no nearby stars or gravitational forces acting on him. Therefore, there are no forces acting on the astronaut.

**Hint:** Think about what happens to the forces when the astronaut is no longer in contact with the spaceship.

### Step 4: Apply Newton's First Law of Motion
According to Newton's first law of motion, an object in motion will remain in motion with the same velocity unless acted upon by a net external force. Since the astronaut is not experiencing any forces after separating from the spaceship, his acceleration must be zero.

**Hint:** Remember that if the net force is zero, the acceleration must also be zero.

### Step 5: Conclusion
Thus, the acceleration of the astronaut the instant after he is outside the spaceship is \(0 \, \text{m/s}^2\).

**Final Answer:** The acceleration of the astronaut after he is outside the spaceship is \(0 \, \text{m/s}^2\).

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