Free-Fall Acceleration and Equations of Motion

Free-Fall Motion

• The magnitude of the free-fall acceleration is 9.8 m/s² (on Earth).
• The direction of the free-fall acceleration is downward, towards the center of the Earth.
• The direction of motion changes when dealing with free-falling motion, as the object's velocity changes from upward to downward.
• The free-fall acceleration is always negative because it's directed downward.

Motion Equations

• In the equation 𝑣 = 𝑣𝑜 − g𝑡, 𝑣 represents the final velocity of an object.
• The maximum height reached by a ball thrown up with an initial speed of 12 m/s can be calculated using the equation.

Scalars and Vectors

• A scalar is a physical quantity with only magnitude and no direction, such as temperature.
• Vectors are represented graphically as arrows, with both magnitude and direction.
• The method of adding vectors geometrically is called the head-to-tail method.
• The vector sum (or resultant) of the vectors AB and BC is represented by the diagonal of the parallelogram formed by the two vectors.

Vector Operations

• Vectors can be added geometrically using the head-to-tail method.
• The correct representation of the vector equation for adding vectors is R = A + B.
• When a vector with the same magnitude but opposite direction is added, it results in a zero vector, which is known as the inverse property.

Vector Components

• To convert a vector to its components, the vector is resolved into its x-axis and y-axis components.
• The x-axis and y-axis components of a vector with a magnitude of 10 and making an angle of 30° with the positive x-axis can be calculated using trigonometry.
• In Example 2, the correct magnitude and direction of vector C with components Cx = 10 and Cy = 5 can be calculated using the Pythagorean theorem.