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Motion in 2 Dimensions Projectile Motion Projectile, any object launched through the air. Projectile, any object launched through the air. Trajectory, the path a projectile takes as it travels through space. Trajectory, the path a projectile takes as it travels through space. The path the trajectory takes depends on the view. The path the trajectory takes depends on the view. The distance it travels is called its range. The distance it travels is called its range.

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Fun, right. The trajectory of any object launched into the air can be broken up into two components, if we ignore air resistance. Vertical = gravitational force The trajectory of any object launched into the air can be broken up into two components, if we ignore air resistance. Vertical = gravitational force Horizontal = applied force Horizontal = applied force Horizontal remains constant while the vertical will either increase or decrease depending on the direction.

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The time an object in free fall takes to hit the ground can be determined by taking the square root of 2d/g The time an object in free fall takes to hit the ground can be determined by taking the square root of 2d/g The distance fallen d = 1/2at 2 The distance fallen d = 1/2at 2 These two equations are derived from the distance with average acceleration equation. The maximum height of a projectile is this same equation with diff variables. These two equations are derived from the distance with average acceleration equation. The maximum height of a projectile is this same equation with diff variables. (Memorize them) (Memorize them)

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Aw, youre tire is all flat and junk. Remember, gravity works on all objects equally. Remember, gravity works on all objects equally. Which ball would hit first: One dropped from a height of 2 meters or another thrown horizontally with a velocity of 20m/s at a height of 2 meters? Which ball would hit first: One dropped from a height of 2 meters or another thrown horizontally with a velocity of 20m/s at a height of 2 meters?

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The horizontal and vertical components can be calculated by the following: The horizontal and vertical components can be calculated by the following: V x = Vo Cos V x = Vo Cos V y = VoSin V y = VoSin At any given point in time is represented by: At any given point in time is represented by: X = V x T = VoCosT X = V x T = VoCosT Y = V y T = VoSinT – 1/2gt 2 Y = V y T = VoSinT – 1/2gt 2

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Range can be found with the equation Range can be found with the equation R = V x T= 2V x V y /g R = V x T= 2V x V y /g Lets try a couple. Lets try a couple.

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Velocity is speed with direction Velocity is speed with direction Acceleration is a change in speed or direction Acceleration is a change in speed or direction Uniform circular motion is the movement of an object at a constant speed around a circle with a fixed radius Uniform circular motion is the movement of an object at a constant speed around a circle with a fixed radius This object would travel at a constant velocity but not at a constant acceleration This object would travel at a constant velocity but not at a constant acceleration

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Objects traveling in a circle accelerate towards the center, centripetal acceleration A c = V 2 /r or A c = 4pi 2 r/T 2 Objects traveling in a circle accelerate towards the center, centripetal acceleration A c = V 2 /r or A c = 4pi 2 r/T 2 The force that causes centripetal acceleration is represented by F = ma c The force that causes centripetal acceleration is represented by F = ma c The time it takes an object to travel around a circle is called the period The time it takes an object to travel around a circle is called the period

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Last but not least, Motion aka velocity is relative to a frame of reference. Motion aka velocity is relative to a frame of reference. Relative velocity is represented by the following: v a/b + V b/c = V a/c Relative velocity is represented by the following: v a/b + V b/c = V a/c To simplify Va/b and Vb/c are similar to x and y components or (a) and (b) in the pythagorean theorem To simplify Va/b and Vb/c are similar to x and y components or (a) and (b) in the pythagorean theorem

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