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A projectile is any object thrown into space and affected by gravity. The analysis of projectile motion includes both horizontal and vertical components of motion, where gravity affects the vertical motion but not the horizontal motion. Using kinematic equations, the trajectory, range, maximum height, and time of flight of projectiles can be calculated.
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Projectile motion is a form of motion experienced by an object that is thrown, launched, or otherwise projected into the air and moves under the influence of gravity. It follows a curved, parabolic trajectory due to the force of gravity acting on the object. There is no propulsion involved after the initial force is applied. Key Characteristics of Projectile Motion: Two-Dimensional Motion : Projectile motion occurs in both the horizontal and vertical directions simultaneously. Horizontal Motion : The horizontal velocity of the object remains constant throughout the motion, as there are no horizontal forces acting on it (ignoring air resistance). Vertical Motion : The vertical motion is influenced by the force of gravity , causing the object to accelerate downward at g=9.8m/s2. Independence of Motions : The horizontal and vertical motions are independent of each other, meaning the horizontal velocity doesn’t affect the vertical velocity. Equations of Projectile Motion: Assuming that air resistance is neglected, the following equations are used for projectile motion. We will break it down into horizontal and vertical components. Horizontal Motion: Where: v0 is the initial velocity. θ is the angle of projection. t is the time. Vertical Motion: Where: g=9.8 m/s2 is the acceleration due to gravity. Time of Flight (Total Time in the Air): The time of flight depends on the initial velocity and the angle of projection. For a projectile launched and landing at the same height:
Range (Horizontal Distance): The range R is the horizontal distance the projectile covers: Maximum Height: The maximum height H the projectile reaches is given by: Problem : A ball is thrown with an initial velocity of 20 m/s at an angle of 30° above the horizontal. Find: The time of flight. The range (horizontal distance). The maximum height the ball reaches. Solution: Step 1: Time of Flight We use the time of flight formula: Substitute the known values: v0=20m/s θ =30∘ g=9.8 m/s Step 2: Range Use the range formula: Substitute the values: Step 3: Maximum Height Use the formula for maximum height: Substitute the values: Final Answer: Time of Flight = 2.04 seconds Range = 35.35 meters Maximum Height = 5.1 meters