Solved Examples of Free Fall: Step-by-Step Solutions

📚 Quick Study Guide

• 🍎 Definition: Free fall is motion under the influence of gravity alone, neglecting air resistance.
• 📏 Acceleration due to gravity (g): Approximately $9.8 \text{ m/s}^2$ near the Earth's surface. This value can be rounded to $10 \text{ m/s}^2$ for simplified calculations in some problems.
• ⏱️ Key Equations:
  • 📍 Velocity: $v = v_0 + gt$ (where $v_0$ is initial velocity)
  • 🛰️ Displacement: $\Delta y = v_0t + \frac{1}{2}gt^2$
  • 💡 Velocity-Displacement Relation: $v^2 = v_0^2 + 2g\Delta y$
• ✨ Important Considerations:
  • ⬆️ Upward motion is usually considered positive, and downward motion negative (or vice versa, but be consistent!).
  • 🛑 At the highest point of a projectile's trajectory, its vertical velocity is momentarily zero.

Practice Quiz

1. A ball is dropped from a height of 45 meters. How long does it take to reach the ground (ignoring air resistance and assuming $g = 10 \text{ m/s}^2$)?
   1. 3 seconds
   2. 4.5 seconds
   3. 9 seconds
   4. 2.1 seconds
2. A stone is thrown vertically upwards with an initial velocity of 20 m/s. What is the maximum height reached by the stone (assuming $g = 10 \text{ m/s}^2$)?
   1. 10 meters
   2. 20 meters
   3. 40 meters
   4. 30 meters
3. An object is dropped from rest. What is its velocity after 3 seconds (assuming $g = 9.8 \text{ m/s}^2$)?
   1. 9.8 m/s
   2. 19.6 m/s
   3. 29.4 m/s
   4. 39.2 m/s
4. A feather and a bowling ball are dropped in a vacuum. Which one hits the ground first?
   1. The feather
   2. The bowling ball
   3. They hit at the same time
   4. It depends on the height
5. A ball is thrown upwards with a velocity of 15 m/s. What is its velocity at the highest point?
   1. 15 m/s
   2. -15 m/s
   3. 9.8 m/s
   4. 0 m/s
6. If an object falls freely for 5 seconds, how far has it fallen (assuming $g = 10 \text{ m/s}^2$)?
   1. 25 meters
   2. 50 meters
   3. 100 meters
   4. 125 meters
7. A skydiver jumps from an airplane. What force is primarily responsible for their acceleration downwards during free fall (ignoring air resistance)?
   1. Air Resistance
   2. Gravity
   3. Lift
   4. Thrust