A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during w

Question

A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is:

Accepted Answer

1. **Analyze Forces:** Air resistance (fluid friction) always opposes the direction of motion (velocity) .
2. **Upward Motion (Ascent):** The body moves upwards. Both gravity ($mg$) and air resistance ($F_{air}$) act downwards. 
   - Net Force: $F_{net} = mg + F_{air}$.
   - Effective Retardation: $a_{ascent} = g + \frac{F_{air}}{m}$.
3. **Downward Motion (Descent):** The body moves downwards. Gravity ($mg$) acts downwards, while air resistance ($F_{air}$) acts upwards.
   - Net Force: $F_{net} = mg - F_{air}$.
   - Effective Acceleration: $a_{descent} = g - \frac{F_{air}}{m}$.
4. **Conclusion:** Since the magnitude of deceleration during ascent ($g + a_{air}$) is greater than the acceleration during descent ($g - a_{air}$), the body takes less time to cover the same distance during the upward journey than the downward journey. Therefore, $t_{ascent} < t_{descent}$ .

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