When you neglect air resistance, what do you observe about the vertical component of the velocity vector throughout the cannonball ’ s trajectory?
Answer
🎯 Vertical Velocity of a Cannonball Without Air Resistance
🧠 Concept Overview
In the study of projectile motion, neglecting air resistance allows us to focus solely on the effect of gravity. The motion of a cannonball fired at an angle consists of two independent components:
- 🔸 A constant horizontal velocity (since no horizontal forces act on it)
- 🔹 A changing vertical velocity (affected by gravity)
🧲 The vertical component of the velocity is constantly changing due to the uniform downward acceleration of gravity (≈ 9.8 m/s²).
📈 What Happens to the Vertical Velocity?
As the cannonball travels through its parabolic path, its vertical velocity behaves as follows:
- 🔺 During Ascent: The vertical velocity decreases steadily as gravity opposes the upward motion.
- 🔵 At the Peak: The vertical velocity is zero — the cannonball stops moving vertically for an instant.
- 🔻 During Descent: The vertical velocity increases in magnitude again, but in the downward direction.
✅ Conclusion: The vertical component of the velocity vector is not constant — it decreases on the way up, becomes zero at the top, and increases (in the negative direction) on the way down.
📘 Physics Behind It
Gravity exerts a constant force downward, which results in a uniform vertical acceleration:
- Acceleration (ay) = -9.8 m/s² throughout the entire motion.
- Time-symmetry: The time taken to reach the peak equals the time taken to fall back to the original height.
⏱️ This symmetry ensures that the speed upward and downward at the same height are equal in magnitude but opposite in direction.
🔄 Summary
- 📉 Vertical velocity decreases due to gravity on the way up.
- ⛰️ Becomes zero at the top of the trajectory.
- 📈 Increases downward after the peak under the influence of gravity.
- 🚫 Air resistance is ignored, so only gravity affects vertical motion.
The vertical velocity is constantly changing due to the effect of gravity, even though the projectile follows a predictable path.