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: 8
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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In Ghana, we see projectile motion everywhere. When a footballer like Mohammed Kudus takes a free-kick, when we throw a stone to knock down a mango, or even when water sprays from a burst pipe, we are witnessing projectile motion. A projectile is any object that is thrown into the air and moves under the influence of gravity alone. One of the most important questions we can ask is, "How far will it go?" In physics, this horizontal distance is called the range. Understanding how to calculate the range is crucial in sports, engineering, and even in farming. In today's lesson, we will learn the principles behind this motion and master the calculation of a projectile's range.
2.1 What is a Projectile? A projectile is any object that is given an initial velocity and then follows a path determined entirely by the effects of gravitational acceleration. Key Assumption: For our calculations at the SHS level, we will ignore air resistance. This is a simplification, but it allows us to understand the fundamental physics. Path: The curved path that a projectile follows is called its trajectory, which is a parabola. 2.2 The Two Components of Projectile Motion The most important idea to understand is that projectile motion can be broken down 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 (`ux`) is constant throughout the flight. The only equation we need for horizontal motion is: Distance = Speed × Time (`x = ux * t`). Vertical Motion (y-direction): The only force acting is gravity, which pulls the object downwards. This causes a constant downward acceleration, `g`. We use the value g = 9.8 m/s² (or sometimes approximate to 10 m/s² for simpler calculations). Since it's downwards, we often write `ay = -g`. The vertical motion is described by the standard equations of uniformly accelerated motion: `vy = uy + ayt` `y = uyt + ½ayt²` `vy² = uy² + 2ayy` 2.3 Deriving the Formula for Range (R)
Let's consider a projectile launched from the ground with an initial velocity u at an angle θ to the horizontal.
Step 1: Resolve the initial velocity. We must first find the initial horizontal and vertical components of the velocity. Initial horizontal velocity, `ux = u cos θ` Initial vertical velocity, `uy = u sin θ`