A boy is sitting in a car moving with uniform velocity. The boy throws a ball vertically upwards which falls back into his hands. A man standing on the road watches the motion of the ball. The path of the motion of the ball will be:

Options

A. a straight line for the man
B. a straight line for the boy
C. a parabola for the man
D. a parabola for the boy

Answer

To solve the problem, we need to analyze the motion of the ball from two different frames of reference: the boy in the car and the man standing on the road.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The boy is sitting in a car that is moving with a uniform velocity \( V_c \).
- The boy throws a ball vertically upwards with an initial velocity \( V \).

2. **Motion of the Ball with Respect to the Boy**:
- From the boy's perspective (inside the car), when he throws the ball upwards, it moves straight up and then comes straight back down to his hands. This is because the ball has the same horizontal velocity as the car, \( V_c \), when it is thrown.

3. **Motion of the Ball with Respect to the Man on the Road**:
- For the man standing on the road, the ball has two components of motion:
- **Vertical Motion**: The ball moves upwards with velocity \( V \) and then comes down due to the acceleration of gravity \( g \).
- **Horizontal Motion**: The ball continues to move horizontally with the same velocity \( V_c \) as the car.

4. **Resultant Path of the Ball**:
- The combination of the upward motion and the horizontal motion means that the ball will follow a parabolic trajectory. This is characteristic of projectile motion, where an object is thrown with an initial velocity at an angle to the horizontal.

5. **Conclusion**:
- The man standing on the road will observe the ball moving in a parabolic path. This is because the ball has both horizontal and vertical components of motion, resulting in a trajectory that is not a straight line but a parabola.

### Final Answer:
The path of the motion of the ball, as observed by the man standing on the road, will be **parabolic**.