A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball

Question

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is not ignored?

Accepted Answer

1. **Forces involved:** Two forces act on the ball: gravity ($mg$) acting vertically downwards and air resistance ($F_r$) acting opposite to the direction of motion .
2. **Upward Motion (Ascent):** The ball moves upward, so air resistance acts downward. The net force is $F_{net} = mg + F_r$. The effective retardation is $a_{ascent} = g + \frac{F_r}{m}$. This results in a rapid decrease in speed (steep negative slope on the speed-time graph).
3. **Downward Motion (Descent):** The ball moves downward, so air resistance acts upward. The net force is $F_{net} = mg - F_r$. The effective acceleration is $a_{descent} = g - \frac{F_r}{m}$. This results in a slower increase in speed (less steep positive slope) compared to the ascent.
4. **Graph Characteristics:** The speed-time graph will have a steeper slope initially (ascent) and a flatter slope later (descent). Additionally, due to energy loss against air resistance, the final speed upon returning to the ground will be less than the initial projection speed, and the time of descent will be greater than the time of ascent.

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