To determine when the weight of a person can be zero, we will analyze each of the given scenarios one by one.
### Step 1: Free Fall
When a person is falling freely, they are in a state of free fall under the influence of gravity. In this case, the only force acting on the person is gravity, which is directed downwards.
- **Net Force Calculation**:
- The gravitational force (weight) acting on the person is \( mg \) (where \( m \) is mass and \( g \) is acceleration due to gravity).
- In free fall, the person and the object they are in (like an elevator) are accelerating downwards at the same rate (g). Therefore, the net force experienced by the person is zero.
Thus, the weight of the person appears to be zero because they are in a state of free fall.
### Step 2: Orbiting in a Satellite
When a person is inside a satellite orbiting the Earth, they are also in a state of free fall. The satellite and the person inside it are both falling towards the Earth due to gravity, but they have a horizontal velocity that keeps them in orbit.
- **Net Force Calculation**:
- The gravitational force is still acting on the person, but since both the satellite and the person are falling together, the person feels weightless.
Thus, in this scenario, the weight of the person is effectively zero.
### Step 3: In an Airplane Flying at High Altitude
When a person is in an airplane flying at a high altitude, the airplane is not in free fall; it is maintaining a level flight or climbing/descending at a controlled rate.
- **Net Force Calculation**:
- The gravitational force is still acting on the person, and the airplane exerts an upward normal force to counteract gravity. Therefore, the person feels their weight.
Thus, the weight of the person in this scenario is not zero.
### Step 4: Riding in a Gas-Filled Balloon
When a person is riding in a gas-filled balloon, the situation depends on the motion of the balloon. If the balloon is ascending with an acceleration less than \( g \), the person will feel a reduced weight, but they will not be weightless.
- **Net Force Calculation**:
- If the balloon is accelerating upwards, the effective weight felt by the person is \( mg - ma \) (where \( a \) is the upward acceleration of the balloon). If the balloon is in free ascent (accelerating upwards at \( g \)), the person would feel weightless, but this is not a typical case.
Thus, the weight of the person in a gas-filled balloon is not zero unless the balloon is in free fall.
### Conclusion
From the analysis:
- The weight of a person can be zero in the following scenarios:
1. He is falling freely (Correct)
2. He is orbiting in a satellite (Correct)
- The weight of a person is **not** zero in the following scenarios:
3. He is in an airplane flying at a high altitude (Incorrect)
4. He is having a ride in a gas-filled balloon (Incorrect)
### Final Answer
The correct options are 1 and 2.
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