Understanding Free Fall
* Definition: Free fall refers to the motion of an object solely under the influence of gravity. This means air resistance is ignored.
* Acceleration: The acceleration due to gravity (g) is constant and acts downwards. On Earth, g ≈ 9.8 m/s².
Modified Equations of Motion
1. Vertical Displacement (s):
* Standard equation: s = ut + ½at²
* Free fall: s = ut + ½gt²
* s = vertical displacement (distance traveled)
* u = initial velocity (usually upwards, so often taken as positive)
* t = time
* g = acceleration due to gravity (always downwards, so often taken as negative)
2. Final Velocity (v):
* Standard equation: v = u + at
* Free fall: v = u + gt
* v = final velocity
3. Relationship between Velocity and Displacement:
* Standard equation: v² = u² + 2as
* Free fall: v² = u² + 2gs
Key Points to Remember
* Direction: Be mindful of the direction of motion and the sign convention used for displacement, velocity, and acceleration.
* Air Resistance: In real-world scenarios, air resistance significantly affects the motion of falling objects. The equations above provide a simplified model.
* Variations: The equations can be modified to account for different initial conditions, such as an object being thrown upwards.
Example
Let's say you throw a ball straight upwards with an initial velocity of 10 m/s. We want to find its displacement after 2 seconds:
* u = 10 m/s (positive, as it's upwards)
* t = 2 s
* g = -9.8 m/s² (negative, as it acts downwards)
Using the equation s = ut + ½gt², we get:
* s = (10 m/s)(2 s) + ½(-9.8 m/s²)(2 s)²
* s = 20 m - 19.6 m
* s = 0.4 m
This means the ball will be 0.4 meters above its initial position after 2 seconds.
Let me know if you'd like more examples or have specific scenarios you'd like to explore!
