# Physics lab 3 - Objective The kinematics of projectile...

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Objective: The kinematics of projectile motion in the Earth’s gravitational field will be studied to gain an understanding of horizontal range, maximum height range, time of flight, and trajectory of the projectile. Introduction This lab studies the motion of a projectile in two dimensions. The gravitational force acts only in the vertical direction in projectile motion, thus the motion is broken into its vertical behavior and its horizontal behavior which exhibits no force and acts independently of the vertical motion. These two independent motions give rise to position as a function of time in component for (x,y), to velocity as a function of time in component form (ax,ay). When time is eliminated between the x and y equations, the trajectory or equation of the path of the projectile is obtained. In order to determine the motion the initial velocity and launch angle of the projectile are used. The range of the projectile, the maximum height of the projectile above the launch point,

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the time of flight of the projectile, and the path (trajectory) that the projectile describes will all be measured in this lab. These will be studied as a function of the launch angle. dv x dt = a x = 0 The projectile is launched with an initial velocity at an angle ( θ ), and that velocity, in the x direction, does not accelerate because there is no outside force acting on it in the horizontal. dx dt = v x = constant = v o cos θ The velocity in the x direction ( v x ¿ is equal to the initial velocity multiplied by the cos θ at which it was launched. θ represents the launch angle. x =( v o cos θ ) t …….…………………..1) The x motion of a projectile is found by taking the velocity in the x direction ( v o cos θ ) and multiplying it by the time of flight (t), in other words, the time that the projectile is in the air. dv y dt = a y =− g The only force acting on the projectile in the y direction is gravity, which is negative because it’s acting downward. dy dt = v y = v o sin θ ¿ The velocity in the y direction is equal to initial vertical velocity ( v o sin θ ) subtracted by gravity (g) multiplied by the time of flight (t). y = ( v o sin θ ) t gt 2 2 ………………….2) To find the y motion of the projectile travels (y), use the second kinematic equation and replace v o with v o sin θ which is the initial vertical velocity. y = x tan θ ( gx 2 ) 2 ( v o cos θ ) 2 ……….……...3) The trajectory of the projectile (y) is achieved by combining equations 1 & 2. The trajectory is a combination of the x and y motions of the projectile.
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