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Projectile Motion Physics Problems + ward ' s science Key Points: 1. Objects that are projected from, and land on the same horizontal surface will have a vertically symmetrical path. 2. The time it takes from an object to be projected and land is called the time of flight. This depends on the initial velocity of the projectile and the angle of projection. 3. When the projectile reaches a vertical velocity of zero, this is the maximum height of the projectile and then gravity will take over and accelerate the object downward. 4. The horizontal displacement of the projectile is called the range of the projectile and depends on the initial velocity of the object. Key Terms: Trajectory: The path of a body as it travels through space Projectile Motion: Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path. The path that the object follows is called its trajectory. Projectile motion only occurs when there is one force applied at the beginning on the trajectory, after which the only interference is from gravity Initial Velocity: The initial velocity can be expressed as x components and y components: u x = u0 • cosθ u y = u0 • sinθ In this equation, u0 stands for initial velocity magnitude and θ refers to projectile angle. Time of Flight: The time of flight of a projectile motion is the time from when the object is projected to the time it reaches the surface. t depends on the initial velocity magnitude and the angle of the projectile: t = (2 • u y / g) t = (2 • u • sinθ) /g Acceleration: In projectile motion, there is no acceleration in the horizontal direction. The acceleration, a, in the vertical direction is just due to gravity, also known as free fall: a x = 0 a y = −g Velocity: The horizontal velocity remains constant, but the vertical velocity varies linearly, because the acceleration is constant. At any time, t, the velocity is: u x = u0 • cosθ u y = u0 • sinθ − (g • t) You can also use the Pythagorean Theorem to find velocity: u = √(u2 x + u2 y ) Displacement: At time t, the displacement components are: x = u • t • cosθ y = u • t • sinθ – 0.5gt2 The equation for the magnitude of the displacement is Δr = √(x2+ y2) Parabolic Trajectory: We can use the displacement equations in the x and y direction to obtain an equation for the parabolic form of a projectile motion: y = tanθ • x – (g/(2 • u2 • cos2θ) • x2