Question:
When you neglect air resistance, what do you observe about the acceleration vector throughout the cannonball’s trajectory?
Detailed Answer:
When air resistance is neglected, the only force acting on a cannonball in motion is the gravitational force. This significantly simplifies the physics of the motion and leads to the following observations:
1. Acceleration Due to Gravity is Constant
The cannonball experiences a constant downward acceleration throughout its flight. This acceleration is denoted by:
\( \vec{a} = (0, -g) \)
Here, \( g \approx 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity, and the coordinate system assumes the x-axis is horizontal and the y-axis is vertical.
2. Horizontal and Vertical Components of Acceleration
- Horizontal Component: Since no horizontal forces act on the cannonball (air resistance is ignored), the horizontal acceleration is zero. Thus, the horizontal velocity remains constant throughout the motion.
- Vertical Component: The vertical acceleration remains at \( -g \), constantly pulling the cannonball downward.
3. Resulting Trajectory Shape
This constant vertical acceleration, combined with a constant horizontal velocity, results in a parabolic trajectory. The parabolic path is a hallmark of projectile motion under uniform gravity without air resistance.
Conclusion:
Throughout the entire flight of the cannonball—from launch to landing—the acceleration vector remains constant in both magnitude and direction. It always points vertically downward with a magnitude of approximately 9.8 m/s².
This constant downward acceleration is solely due to gravity and is independent of the cannonball’s velocity or position in the air. The behavior is symmetric around the peak of the trajectory.