Free Fall in Projectile Motion: Definition and Examples

📚 Quick Study Guide

• 🍎 Definition: Free fall refers to the motion of an object where the only force acting upon it is gravity. In projectile motion, this means after the object is launched, gravity is the only force affecting its vertical motion.
• 📏 Assumptions: We typically ignore air resistance for simplicity.
• 📉 Vertical Motion: The vertical acceleration ($a_y$) is equal to the acceleration due to gravity ($g$), which is approximately $9.8 m/s^2$ downwards (often taken as positive or negative depending on the chosen coordinate system).
• ↔️ Horizontal Motion: Assuming no air resistance, the horizontal velocity ($v_x$) remains constant.
• 📝 Key Equations:
  • Vertical displacement: $\Delta y = v_{iy}t + \frac{1}{2}gt^2$
  • Final vertical velocity: $v_{fy} = v_{iy} + gt$
  • Time of flight (for projectile landing at the same height): $t = \frac{2v_{iy}}{g}$
  • Range (horizontal distance): $R = v_{ix}t = v_{ix}\frac{2v_{iy}}{g}$ (only if landing at same height as launch)

Practice Quiz

1. What is the only force acting on an object in free fall (ignoring air resistance)?
   1. A) Applied Force
   2. B) Tension
   3. C) Gravity
   4. D) Normal Force
2. What is the vertical acceleration of a projectile in free fall (ignoring air resistance)?
   1. A) 0 m/s²
   2. B) 4.9 m/s² upwards
   3. C) 9.8 m/s² downwards
   4. D) 9.8 m/s² upwards
3. A ball is thrown upwards. At its highest point, what is its vertical velocity?
   1. A) 9.8 m/s
   2. B) -9.8 m/s
   3. C) 0 m/s
   4. D) It depends on the initial velocity
4. A projectile is launched horizontally. How does its horizontal velocity change during its flight (ignoring air resistance)?
   1. A) Increases constantly
   2. B) Decreases constantly
   3. C) Remains constant
   4. D) Changes direction
5. If a projectile is launched at an angle, what happens to its vertical velocity as it rises?
   1. A) Increases
   2. B) Decreases
   3. C) Remains constant
   4. D) Becomes zero and then increases in the opposite direction
6. Two balls are released from the same height at the same time. One is dropped, and the other is thrown horizontally. Which one hits the ground first (ignoring air resistance)?
   1. A) The dropped ball
   2. B) The thrown ball
   3. C) They hit at the same time
   4. D) It depends on the initial horizontal velocity
7. A projectile is launched upwards with an initial vertical velocity of 20 m/s. What is its vertical velocity after 2 seconds (assume g = 10 m/s²)?
   1. A) 0 m/s
   2. B) 10 m/s
   3. C) -20 m/s
   4. D) -40 m/s