Data table 8 relationship between range and time

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Data Table 8: Relationship between Range and Time Angle Measure Average Maximum Height (cm) Average Time(seconds) 0 0.26 15° 3.5 0.34 30° 13.6 0.51 45° 26.6 0.56 60° 37.2 0.58 90° 50 0.57 Data Table 9: Calculations of Vertical Velocity Angle Measure Vertical Velocity (cm/s) 0.001274 cm/s 15° 0.001666 cm/s 30° 0.002499 cm/s 45° 0.002744 cm/s 60° 0.002842 cm/s 90° 0.002793 cm/s Relation to Kinematic Equations: In this experiment time is found in order to find the (initial) vertical velocity. The vertical velocity can be found using the equation Vf = Vi + at : in which the product of (t) time and a ( the acceleration of gravity) is proportional to the final velocity (Vf). In this instance, Vf and a and t known, but not the initial vertical velocity (Vi) Since the projectile is being launched upwards, there is a gravitational force on the object, creating an acceleration of 9.8 m/s/s; however, since all the calculations are in centimeters, the force of gravity is 0.0098 cm /s/s. When at its maximum height, the velocity is zero. An object usually reaches max height on the midpoint of the journey. Therefore, to calculations; divide the time by 2 and use Vf=0 in order to calculate Vi. 11
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Sample Calculations: EX) Total Time: 0.34 0 = Vi+(-0.0098 cm/s/s)(0.34*0.5) Final Velocity (Vf)= ) Isolate V i by subtracting Vi from both sides Vi x : ? -Vi = -0.001666 cm/s Vi= 0.001666 cm/s 12
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PART TWO CONCLUSIONS 13
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14
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Conclusions Conclusion for Objective 1 As displayed by Data Graph 1: Average of Launch Angle and Height , there is a direct relation between launch angle and height. An analysis of the velocity components for these projectiles is needed to understand this concept of linearly related variables. The peak height of a projectile is determined by the initial value of the vertical velocity component. The greater the initial value of Vy, the higher that a projectile will rise. The projectile launched at 60-90 degrees has the greatest Vy, and as such the greatest peak height. As you can see from Data Graph 1, the larger the initial launch angle, the closer the object comes to maximum height and the longer the flight time. Conclusion for Objective 2 As seen from Data Graph 2: Average of Launch Angle and Range, the relationship between launch angle and range is parabolic, inversely. The ball launched at a 45-degree angle had the greatest range, which is shown by the peak of the parabola in Data Graph 2. The range of a projectile is determined by two parameters: the initial value of the horizontal velocity component and the “hang time” of the projectile. The projectile launched at 45- degree achieves the greatest range. This means that the range of a projectile (assuming the initial velocity is constant) will increase and be at maximum until the launch angle is 45 degrees. If the launch angle is greater than 45 degrees, then the range becomes lesser, as shown in Data Graph 2.
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  • Winter '14
  • jane smith
  • Trajectory, Velocity, Right angle

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