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**Motion in 2 Dimensions Projectile Motion**

Projectile, any object launched through the air. Trajectory, the path a projectile takes as it travels through space. The path the trajectory takes depends on the view. 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 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 distance fallen d = 1/2at2 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)

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**Aw, you’re tire is all flat and junk.**

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?

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**The horizontal and vertical components can be calculated by the following:**

Vx= Vo Cos Vy = VoSin At any given point in time is represented by: X = VxT = VoCosT Y = VyT = VoSinT – 1/2gt2

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**Range can be found with the equation**

R = VxT= 2VxVy/g Lets try a couple.

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**Velocity is speed with 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 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 Ac = V2/r or Ac= 4pi2r/T2 The force that causes centripetal acceleration is represented by F = mac 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. Relative velocity is represented by the following: va/b + Vb/c = Va/c 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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Motion in Two Dimensions

Motion in Two Dimensions

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