Free fall

1. Understanding Free Fall

• Free fall is the motion of an object under the influence of gravitational force only, with no air resistance.
• Objects in free fall experience constant acceleration due to gravity.

Gravitational Acceleration $(g)$

• Definition: The acceleration of a freely falling object due to gravity.
• On Earth: $g = :highlight[9.8] \text{ m/s}^2$ (rounded to $:highlight[9.8]$ in calculations).
• On the Moon: $g = :highlight[1.6] \text{ m/s}^2$
• Gravity always acts downwards towards the centre of the Earth.

2. Equations for Free Fall

Use the following kinematic equations:

1. $v_f = v_i + a\Delta t$

2. $v_f^2 = v_i^2 + 2a\Delta y$

3. $\Delta y = v_i\Delta t + \frac{1}{2} a\Delta t^2$

Where:

• $v_f =$ final velocity (m/s)
• $v_i =$ initial velocity (m/s)
• $\Delta y =$ displacement (m)
• $a =$ acceleration due to gravity (m/s²)
• $\Delta t =$ time (s)

3. Tips for Solving Free-Fall Problems

• Use acceleration due to gravity as $:highlight[9.8] \text{ m/s}^2$ unless stated otherwise.
• Ignore air resistance, unless the question specifies otherwise.
• Choose a positive direction (up or down) and remain consistent throughout the problem.
• If upwards is positive, gravitational acceleration $(g)$ will be negative.
• If downwards is positive, gravitational acceleration $(g)$ will be positive.

4. Key Takeaways

• Free fall is motion under gravity alone.
• Acceleration due to gravity is constant at $:highlight[9.8] \text{ m/s}^2.$
• Always define direction before solving.
• Use kinematic equations to calculate motion parameters.