Memorandum Design 4 Practice D4P Program For 186 Students

Memorandumdesign4practice D4p Programtoegr 186 Studentsfromdr Ost

Memorandum Design4Practice (D4P) Program To: EGR 186 Students From: Dr. Ostroha Date: March 23, 2015 Re: Using Excel – Airplane Cargo Drop This assignment is due at the beginning of next class. Excel is available in many computer labs across campus. Using formulas, absolute addresses, and x-y plot: Supplies are dropped from an airplane to land at a certain point. The velocity of the package at release from the airplane is the speed of the airplane, v0x=200ft/s. The acceleration of the package due to gravity is ay = -32.2 ft/s2. The displacement in the y direction can be found using the following equation: y - y0 = v0yt + ½ayt2. The final position of the package (y) is on the ground, and y0 represents the height of the plane when the package is dropped. The initial velocity in the y direction (v0y) is zero. Therefore, the equation becomes: y = y0 + ½ayt2. The distance the package travels in the x direction can be found from the equation: x - x0 = v0xt + ½axt2. The final position of the package (x) is measured from the initial position (x0). If x0 is taken as zero, and if the plane is traveling at a constant speed (ax is zero), then the equation becomes: x = v0xt. Solve this problem using Excel (it may help to print this page and cross off the directions as you complete them).

Paper For Above instruction

The given problem involves calculating the trajectory of a package dropped from an airplane using Excel. The core idea is to model the horizontal and vertical motions separately and then combine the results to determine when and where the package hits the ground. The initial data includes the height of the airplane, the velocity of the plane, and the acceleration due to gravity. The calculations involve standard kinematic equations, implemented via formulas in Excel, which allow for dynamic adjustments and visualizations through graphs.

First, the initial data cell table helps organize relevant parameters: the plane's height (300 ft), acceleration due to gravity (-32.2 ft/sec²), and plane velocity (200 ft/sec). These parameters are essential for setting up the equations governing the motion.

Next, the data table is created with columns for time (t), horizontal position (x), and vertical position (y). Starting at t=0 seconds, the time increments in 0.5-second intervals for the duration of the calculation. The formulas for x and y are input into Excel cells using absolute references to lock in the initial data, ensuring the formulas adapt for each time increment. The formula for x is straightforward: x = v0x * t, since acceleration in the x-direction is zero, assuming the airplane maintains a constant speed.

In contrast, the vertical position y is computed from the initial height y0, initial vertical velocity (zero), and acceleration due to gravity, following y = y0 + ½ ay t^2. This equation models the downward displacement over time. The cell formulas are copied down the columns to generate a series of (t, x, y) data points.

Graphical visualizations involve plotting x vs. t and y vs. t separately to observe the motion over time. Creating these charts involves selecting the relevant data range and inserting line charts with markers, enhancing clarity with proper labels, titles, gridlines, and axis labels including units. Removing the legend helps focus on the data series, and formatting the axes ensures precise interpretation.

Additionally, a combined chart with both x and y plotted against t illustrates the trajectory in a two-dimensional space, providing a comprehensive view of the package's path. Series labels are edited to clearly distinguish between horizontal and vertical distances, and graph titles clarify the content.

The critical part of the analysis involves determining when the package hits the ground (y=0). Using trial and error, one can manually check at which time the height approaches zero. For a more efficient method, Excel's Goal Seek feature automates this process. By setting the cell representing y at the final time (y at t) to zero, and allowing the adjustment of time, Goal Seek provides the exact moment the package reaches ground level. This time value is recorded in the spreadsheet for reporting.

Finally, the results—charts, data tables, and the computed landing time—are compiled into a Word document. The data tables and graphs are pasted as pictures with captions explaining their significance. The text discusses each graph's insights, such as the upward parabolic shape of y(t) indicating free fall and the linear nature of x(t) confirming constant velocity. The goal seek output reinforces the theoretical calculation of the impact time, validating the model.

In conclusion, modeling projectile motion in Excel offers valuable insights into kinematic processes. The combined use of formulas, data visualization, and goal-seeking functions enables a comprehensive analysis, demonstrating mechanics principles and enhancing understanding through practical application.

References

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• Microsoft Support. (2023). Create a line chart in Excel. Retrieved from https://support.microsoft.com
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