A bicyclist is riding at a constant speed along a straight-line path. The rider throws a ball straight up to a height a few meters above her head. Ignoring air resistance, where will the ball land?

Options

A. Behind the rider
B. In front of the rider
C. In the same hand that threw the ball
D. In the opposite hand to the one that threw it.

Answer

To solve the problem of where the ball will land when thrown straight up by a bicyclist moving at a constant speed, we can break it down into a few logical steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The bicyclist is moving at a constant speed (let's denote this speed as \( V \)).
- The ball is thrown straight up from the bicyclist's hand.

2. **Analyzing the Motion of the Ball**:
- When the ball is thrown upward, it has an initial vertical velocity (let's denote this as \( V_{y0} \)), which is the speed at which the ball is thrown upwards.
- However, the ball also retains the horizontal velocity of the bicyclist, which is \( V \).

3. **Vertical Motion**:
- The vertical motion of the ball will be influenced by gravity, which acts downward with an acceleration of \( g \).
- The ball will rise to a maximum height, where its vertical velocity becomes zero, and then it will fall back down.

4. **Horizontal Motion**:
- Since there is no horizontal acceleration acting on the ball (ignoring air resistance), it will continue to move horizontally at the same speed \( V \) as the bicyclist.
- This means that while the ball is in the air, it will travel horizontally the same distance as the bicyclist.

5. **Time of Flight**:
- The time the ball spends in the air is determined by its vertical motion. It will take some time to reach the maximum height and then the same amount of time to fall back down.
- During this time, the bicyclist continues to move forward at speed \( V \).

6. **Conclusion**:
- Since both the ball and the bicyclist have the same horizontal velocity, when the ball comes back down, it will land directly back in the hand of the bicyclist.

### Final Answer:
The ball will land directly back in the hand of the bicyclist.

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