Lecture on Vertical Motion

Key Concepts

Position, Velocity, and Acceleration: Understanding the basic parameters of motion.
Kinematic Equations: Governing the relationships between position, velocity, and acceleration.
Application to both horizontal and vertical motion.

Acceleration due to Gravity:
- Constant value: -9.8 m/s² (unique to Earth).
- Direction: Always towards the Earth (i.e., negative direction).
Direction Convention:
- Positive/Negative arbitrary in horizontal motion.
- Negative direction always downwards in vertical motion.
Scenarios in Vertical Motion:
- Free fall (dropped from a standstill).
- Initial upward velocity.
Non-Earth Scenarios: Different gravity values.

Calculate Time of Free Fall
- Initial velocity ( (v_0)) = 0
- Displacement ((d)) = -100 m (negative due to direction)
- Using kinematic equation for position: [d = v_0 t + \frac{1}{2} a t^2]
- Acceleration ( (a)) = -9.8 m/s²
- Solving for time ( (t)): (t \approx 4.5\sec)
Calculate Velocity Upon Impact
- Use kinematic equation for velocity: [v = v_0 + a t]
- Initial velocity ( (v_0)) = 0
- Acceleration ( (a)) = -9.8 m/s²
- Time ( (t)) = 4.5 sec
- Final velocity ( (v)): (v \approx -44.1 m/s)

Calculate Total Travel Time
- Initial upward velocity ( (v_0)) = 10 m/s
- Displacement ((d)) = -100 m
- Using standard kinematic equation: [d = v_0 t + \frac{1}{2} a t^2]
- Acceleration ( (a)) = -9.8 m/s²
- Solve quadratic equation for time ( (t)): Two solutions, discard the negative one.
- Total travel time ( (t)): (t \approx 5.65\sec)
Calculate Velocity Upon Impact
- Use kinematic equation for velocity: [v = v_0 + a t]
- Initial velocity ( (v_0)) = 10 m/s
- Acceleration ( (a)) = -9.8 m/s²
- Time ( (t)) = 5.65 sec
- Final velocity ( (v)): (v \approx -45.4 m/s)

Notes