Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Apply equations of motion to solve vertical projectile problems.
• Use mole concepts to solve stoichiometric problems.
• Perform calculations using balanced chemical equations.
• Analyse graphs related to motion and reaction rates.
• Evaluate the impact of stoichiometry in industry.

Lesson summary

This week focuses on intensive revision and examination preparation for the following key areas: Vertical Projectile Motion (1D), and Quantitative aspects of Chemical Change (Stoichiometry). These are fundamental concepts that not only form the basis for further studies in science and engineering but also have direct relevance to everyday life in South Africa, from understanding the trajectory of a ball thrown by a child to the precise calculations needed in chemical industries that produce fertilisers and pharmaceuticals. A strong grasp of these topics is crucial for achieving success in the final examinations.

Lesson notes

2.1 Vertical Projectile Motion (1D)

Definition: Projectile motion refers to the motion of an object projected into the air, subject only to the acceleration of gravity (neglecting air resistance, unless stated otherwise). In the case of vertical projectile motion, the object's movement is restricted to the vertical axis (up and down).

Key Concepts: Acceleration due to gravity (g): This is the constant acceleration acting downwards on any object near the Earth's surface. In South Africa, we use g = 9.8 m/s². Remember to choose a consistent sign convention (upwards as positive or downwards as positive) and stick to it throughout your calculations. The sign of 'g' depends on the chosen sign convention. If upward is positive, g = -9.8 m/s². If downward is positive, g = 9.8 m/s².

Initial velocity (vi): The velocity of the object at the moment it is projected.

Final velocity (vf): The velocity of the object at a specific point in its trajectory. Displacement (Δy): The change in position of the object. Time (Δt): The duration of the motion.

Equations of Motion: These are the fundamental equations that describe the relationship between the variables mentioned above: vf = vi + aΔt Δy = viΔt + ½a(Δt)² vf² = vi² + 2aΔy Δy = (vi + vf)/2 * Δt Where: vf = final velocity vi = initial velocity a = acceleration (in this case, 'g') Δt = change in time Δy = change in displacement (vertical height)

Important Considerations: At the highest point of the trajectory, the vertical velocity (vf) is zero. The time taken to reach the highest point is equal to the time taken to fall back to the initial height (if air resistance is negligible). The velocity at which the object returns to the initial height is equal in magnitude but opposite in direction to the initial velocity (again, neglecting air resistance).