Lesson Notes By Weeks and Term v4 - SHS 2
KINEMATICS
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KINEMATICS
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 9
Grade code: 2.1.3.LI.3
Strand code: 1
Sub-strand code: 3
Content standard code: 2.1.3.CS.1
Indicator code: 2.1.3.LI.3
Theme: MECHANICS AND MATTER
Subtheme: KINEMATICS
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Today, we are going to explore one of the most exciting parts of kinematics: projectile motion. Think about a footballer like Mohammed Kudus taking a free kick, an athlete in a long jump competition, or even the simple act of throwing a stone into a river. All these are examples of projectiles. Understanding how to calculate their motion, specifically how far they travel horizontally, is not just for passing exams. It is fundamental to sports science, engineering, and even military applications. By the end of this lesson, you will be able to predict the horizontal distance an object will travel when launched into the air.
What is a Projectile? A projectile is any object that is thrown or projected into the air and then moves under the influence of gravity alone.
Key Assumptions (for SHS Physics): We neglect air resistance. In reality, air slows things down, but for our calculations, we will assume it has no effect. The acceleration due to gravity, g, is constant (approximately 9.8 m/s² or 10 m/s² for calculations) and acts vertically downwards.
The path followed by a projectile is a curve called a trajectory, which is parabolic in shape. Components of Projectile Motion The most important concept to understand is that we analyse the motion of a projectile by splitting it into two separate, independent parts: Horizontal Motion (x-direction): Since we ignore air resistance, there is no force acting horizontally. According to Newton's First Law, this means there is no horizontal acceleration (aₓ = 0). Therefore, the horizontal velocity is constant throughout the flight. Equation: `Horizontal Distance = Horizontal Velocity × Time` Vertical Motion (y-direction): The only force acting is gravity, which pulls the object downwards. This causes a constant downward acceleration, `aᵧ = -g`. (We use '-' to show it's downwards). The vertical velocity changes continuously: it decreases as the object goes up, becomes zero at the maximum height, and increases as the object comes down. We use the standard equations of motion for this part: `v = u + at` `s = ut + ½at²` `v² = u² + 2as` Deriving the Formula for Range
Let's consider a projectile launched with an initial velocity u at an angle θ to the horizontal.