Free Fall Problems - Physics Lecture

Introduction

Focus on analyzing free fall problems using kinematic equations.
Three problem types:
1. Dropping an object from a height.
2. Throwing an object up and analyzing its motion.
3. Throwing an object down from a height.
Use of 1D motion and constant acceleration due to gravity.

Applicable under 1D motion and constant acceleration.
Equations:
1. $v_{final} = v_{initial} + at$
2. $\Delta y = v_{initial} , t + \frac{1}{2} a t^2$
3. $v_{final}^2 = v_{initial}^2 + 2a \Delta y$
For free fall, set $a = -g$, where $g = 9.8 , m/s^2$.
Negative sign indicates downward direction.

Setup: Object dropped from a height of 7 meters.
Key Points:
- Initial velocity $v_{initial} = 0 , m/s$.
- Use kinematic equations to find time to impact and final velocity.
Equations Used:
- $\Delta y = \frac{1}{2} (-g) t^2$ to find time.
- $v_{final} = -gt$ to find velocity before impact.

Setup: Object thrown up from 7 meters at 6 m/s.
Key Points:
- Velocity at peak (top) is 0 m/s.
- Solve for time to reach peak and maximum height.
Questions Addressed:
1. Time to Top: Use $v_{final} = v_{initial} - gt$.
2. Maximum Height: Use $\Delta y = v_{initial} , t - \frac{1}{2} gt^2$.
3. Speed before Ground Impact: Use $v_{final}^2 = v_{initial}^2 - 2g \Delta y$.
4. Total Flight Time: Solve using quadratic equations or add up/down times.

Setup: Object thrown down from 7 meters at 8 m/s.
Key Points:
- Initial velocity is negative due to downward direction.
Questions Addressed:
1. Time to Ground: Solve quadratic $\Delta y = v_{initial} , t - \frac{1}{2} gt^2$.
2. Velocity before Ground Impact: Use either $v_{final} = v_{initial} - gt$ or $v_{final}^2 = v_{initial}^2 + 2g \Delta y$.