Solved examples of Free Fall Symmetry: Calculating Initial Velocity

📚 Quick Study Guide

• ⏱️ The time it takes an object to reach its maximum height in free fall is equal to the time it takes to fall back to its initial height.
• 📍 At the maximum height, the object's velocity is momentarily zero ($v = 0$).
• 📉 Acceleration due to gravity ($g$) is constant and approximately $9.8 m/s^2$ (or $10 m/s^2$ for simpler calculations) and acts downwards.
• 🚀 Initial velocity ($v_0$) and final velocity ($v_f$) at the same height have the same magnitude but opposite signs (assuming no air resistance).
• 📐 Key Equation: $v_f = v_0 - gt$, where $v_f$ is final velocity, $v_0$ is initial velocity, $g$ is acceleration due to gravity, and $t$ is time.

Practice Quiz

1. A ball is thrown vertically upwards and returns to its starting point after 4 seconds. What was its initial velocity? (Assume $g = 10 m/s^2$)
   1. 10 m/s
   2. 20 m/s
   3. 30 m/s
   4. 40 m/s
2. An object is thrown upwards with an initial velocity of 25 m/s. How long will it take to reach its maximum height? (Assume $g = 10 m/s^2$)
   1. 1.5 seconds
   2. 2 seconds
   3. 2.5 seconds
   4. 3 seconds
3. A stone is tossed upwards. If its velocity is 0 m/s after 3 seconds, what was the initial velocity? (Assume $g = 10 m/s^2$)
   1. 10 m/s
   2. 20 m/s
   3. 30 m/s
   4. 40 m/s
4. A projectile launched upwards takes 6 seconds to return to the launch point. What is the time taken to reach the maximum height?
   1. 6 seconds
   2. 2 seconds
   3. 3 seconds
   4. 4 seconds
5. If a ball is thrown upwards with a speed of 15 m/s, what is the speed of the ball when it returns to the thrower's hand? (Assume no air resistance)
   1. 5 m/s
   2. 10 m/s
   3. 15 m/s
   4. 20 m/s
6. What is the initial velocity of a ball thrown upwards if it reaches a height of 5 meters? (Assume $g = 10 m/s^2$ and neglect air resistance. Use the equation $v_f^2 = v_i^2 + 2ad$)
   1. 5 m/s
   2. 10 m/s
   3. 15 m/s
   4. 20 m/s
7. A ball thrown upwards returns to its starting point after 8 seconds. Calculate its initial velocity. (Assume $g = 10 m/s^2$)
   1. 20 m/s
   2. 30 m/s
   3. 40 m/s
   4. 50 m/s