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The problem asks to identify which pair of graphs represents the horizontal motion of a ball dropped by a bicycle rider moving to the right at constant speed.

### Key Concepts:
1. **Horizontal motion**: When the ball is dropped, it maintains the same horizontal velocity as the bicycle because there is no horizontal force acting on it (assuming air resistance is negligible).
   
2. **Constant horizontal velocity**: Since the bicycle moves at constant speed, the ball will continue moving horizontally with that same speed.

#### Analyzing the options:
- **Distance vs. Time (horizontal)**: The distance covered by the ball horizontally increases linearly over time because the horizontal velocity remains constant.
  
- **Speed vs. Time (horizontal)**: Since the horizontal speed does not change, the speed-time graph should be a horizontal line.

#### Correct Answer: **Option B**
- The **distance-time** graph in option B shows a straight line with constant slope, representing constant speed.
- The **speed-time** graph in option B is a horizontal line, representing constant horizontal speed.

Would you like a more detailed breakdown or have any questions?

### Related Questions:
1. How would the vertical motion of the ball be represented after being dropped?
2. What would happen to the ball's horizontal motion if air resistance were considered?
3. How does this problem illustrate Newton's First Law of Motion?
4. How would the graph change if the bicycle were accelerating?
5. What role does the initial horizontal velocity play in projectile motion?

**Tip**: In projectile motion, horizontal and vertical motions are independent of each other, which is why the horizontal velocity remains constant when no forces are acting horizontally.

A bicycle rider traveling to the right at a constant speed drops a ball. Which of the following pairs of graphs best represents the horizontal motion of the ball relative to the ground?

This problem involves analyzing the horizontal motion of a ball dropped from a bicycle traveling at constant speed. Learn about the key physics concepts of horizontal motion, constant velocity, and Newton's First Law. Suitable for high school students in grades 9-12.

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