Projectile Motion and Related Calculations - SS2 Physics Lesson Note
Projectile motion refers to the motion of an object launched into the air and subject only to the force of gravity and air resistance (if present). It follows a curved path known as a projectile trajectory.
Key Concepts:
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Horizontal and Vertical Motions: In projectile motion, the object moves horizontally with a constant velocity, while vertically, it experiences acceleration due to gravity.
Independence of Motions: The horizontal and vertical motions are independent of each other. The horizontal motion remains unaffected by gravity, while the vertical motion is solely influenced by gravity.
Parabolic Trajectory: The path followed by a projectile is a parabola. The shape and size of the parabola depend on the initial velocity, launch angle, and height from which the object is launched.
Equations for Projectile Motion:
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Horizontal Motion: The horizontal velocity remains constant throughout the motion, and the horizontal displacement (x) is given by, x = v₀ x t, where v₀x is the initial horizontal velocity and t is the time.
Vertical Motion: The vertical displacement (y), velocity (vy), and time (t) can be calculated using the following equations:
y = v₀y t - (1/2) g t²
vy = v₀y - g t
t = 2 v₀y / g (time of flight)
vy² = v₀y² - 2 g y (final vertical velocity)
Projectile Motion Calculations:
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Range: The range is the horizontal distance covered by the projectile before it hits the ground. It can be calculated as, R = (v₀² sin(2θ)) / g, where θ is the launch angle.
Maximum Height: The maximum height reached by the projectile can be calculated as H = (v₀y²) / (2 x g).
Time of Flight: The total time of flight is the time taken by the projectile to reach the ground. It is given by T = (2 x v₀y) / g.
Projectile Velocity: The magnitude of the velocity (v) at any point can be calculated using the Pythagorean theorem: v = √(vx² + vy²).
Factors Affecting Projectile Motion:
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Launch Angle: The angle at which the projectile is launched determines the shape of the trajectory and affects the range and maximum height.
Initial Velocity: The initial velocity determines the overall magnitude of the projectile's velocity and influences the range and maximum height.
Air Resistance: In the absence of air resistance, projectile motion follows idealised calculations. However, air resistance can affect the trajectory and decrease the range.
Applications of Projectile Motion:
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Sports: Projectile motion is crucial in sports such as baseball, basketball, and soccer, where players need to accurately project the trajectory of the ball.
Physics Experiments: Projectile motion is often studied in physics laboratories to understand concepts of motion, kinematics, and gravity.
Engineering: Understanding projectile motion is essential in fields such as aerospace engineering, where the trajectory of rockets, missiles, and satellites must be accurately predicted.
Projectile motion is a fundamental concept in physics that provides insights into the motion of objects in the presence of gravity. By understanding the equations and calculations associated with projectile motion, we can analyse and predict the behaviour of projectiles in various real-world scenarios.