Solved Examples of Free Fall Motion with Constant Acceleration

📚 Quick Study Guide

🔍 Free Fall: Motion under the influence of gravity only (neglecting air resistance). 🍎 Acceleration due to gravity (g): Approximately $9.8 m/s^2$ near the Earth's surface. Often rounded to $10 m/s^2$ for simplicity. 💡 Equations of Motion (Constant Acceleration):
• Displacement: $d = v_0t + \frac{1}{2}at^2$
• Final Velocity: $v = v_0 + at$
• Velocity-Displacement Relation: $v^2 = v_0^2 + 2ad$
⌚ Key Assumptions: Constant acceleration, negligible air resistance, motion in one dimension.

🧪 Practice Quiz

1. A ball is dropped from a height of 45 meters. How long does it take to reach the ground? (Assume $g = 10 m/s^2$)
   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? (Assume $g = 10 m/s^2$)
   1. 10 meters
   2. 20 meters
   3. 30 meters
   4. 40 meters
3. An object is in free fall. What is its velocity after 3 seconds, assuming it starts from rest? (Assume $g = 10 m/s^2$)
   1. 10 m/s
   2. 20 m/s
   3. 30 m/s
   4. 40 m/s
4. A ball is thrown downwards with an initial velocity of 5 m/s from a height of 15 meters. What is its final velocity just before hitting the ground? (Assume $g = 10 m/s^2$)
   1. 10 m/s
   2. 15 m/s
   3. 20 m/s
   4. 25 m/s
5. If an object takes 5 seconds to fall freely to the ground from a certain height, what is the height from which it was dropped? (Assume $g = 10 m/s^2$)
   1. 50 meters
   2. 75 meters
   3. 100 meters
   4. 125 meters
6. A feather and a stone are dropped simultaneously in a vacuum. Which one will reach the ground first?
   1. The feather
   2. The stone
   3. Both will reach at the same time
   4. It depends on the shape of the feather
7. An object is projected upwards with a velocity of 30 m/s. What is the time taken to reach the maximum height? (Assume $g = 10 m/s^2$)
   1. 1 second
   2. 2 seconds
   3. 3 seconds
   4. 4 seconds