5_pdfsam_1 - g = 32 2 ft/s 2 directed in negative y...

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Output or results to be produced: It is clear from the problem statement that the results to be produced are the time of flight and the distance traveled. The units for these quantities haven’t been speciFed, but from our knowledge of throwing a baseball, computing time in seconds and distance in feet would be reasonable. Theoretical and experimental knowledge to be applied: The theory to be applied is that of ballistic motion in two dimensions. Input information or data: This includes the object initial velocity of 50 miles per hour at an angle 30 degree above horizontal. 2. Mathematical Model: To pose this problem in terms of a mathematical model, we Frst need to deFne the notation: Time: t (s), with t = 0 when the object is launched. Initial velocity magnitude: v = 50 miles/hour. Initial angle: θ =30 . Horizontal position of ball: x ( t ) (ft). Vertical position of ball: y ( t ) (ft). Acceleration of gravity:
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Unformatted text preview: g = 32 . 2 ft/s 2 , directed in negative y direction. The key step in developing a mathematical model is to divide the trajectory into its horizontal and vertical components. The initial velocity can be divided in this way, as shown in ±igure 1.1. ±rom basic trigonometry, we know that v h = v cos θ v v = v sin θ ±igure 1.1: Initial velocity ( v ) divided into horizonal ( v h ) and vertical ( v v ) components. Given the horizontal and vertical components of the initial velocity, the horizontal and vertical positions can be determined as functions of time. Since there is no external force acting to retard the horizontal motion, the object will move at a constant speed of v h in the horizontal direction x ( t ) = vt cos θ In the vertical direction, the object motion is retarded by gravity and its position is y ( t ) = vt sin θ − 1 2 gt 2 5...
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This note was uploaded on 03/07/2010 for the course ENG 101 taught by Professor Chang during the Summer '09 term at 東京国際大学.

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