Jensen_Grant_Project2.pdf

# Rng x1000 converts the x values from meters to

• 18

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rng = x/1000; %Converts the x values from meters to kilometers rng = max(rng); %This makes it so only the maximum range is graphed, which makes it much easier for the computer f_t = max(t); %This makes it so only the total time is graphed, which makes it much easier for the computer %Calls the plot_range function to create the x vs k and t vs k graphs

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Flight Path of a Projectile 10 [krng , kf_t] = plot_range( rng , k(j) , f_t ); end plot_range.m function [ krng, kf_t ] = plot_range( rng , k , f_t ) %Grant Jensen, AER E 161, Project #2, plot_range %Plots graphs for range %Graphs Range(x) vs Air Resistance(k) and %Total flight time(t) vs Air Resistance(k) %To call the function: plot_range(x,k,t) %Input arguments: x, k, t %Where: rng is a value of range % k is air resistance % f_t is a value of time %Outputs: graphs of k vs range and k vs f_t %Next 8 lines create the range vs air resistance graph figure(5) ; %Creates a new figure. It is index as 5 because the graphs from plot_flightpaths have already taken up 4 new figures krng = plot(k,rng, '.b' ); %Plots graph with blue * points title( 'Range vs Air Resistance' ); %Creates the title for the 1st graph ylabel( 'Range ( km )' ); %Labels the y-axis xlabel( 'k (s^-^1)' ); %Labels the x-axis xlim([0 0.08]) %Sets the limits of the x-axis as 0 and 0.08 ylim([0 35]) %Sets the limits of the y-axis as 0 and 35 hold on %Holds all values of x and k %Next 8 lines create the total flight time vs air resistance graph figure(6); %Creates a new figure kf_t = plot(k,f_t, '.b' ); %%Plots the 2nd graph with blue * points title( 'Total flight time vs Air Resistance' ) %Creates the title for the 2nd graph ylabel( 'Flight time (s)' ); %Labels the y-axis xlabel( 'k (s^-^1)' ); %Labels the x-axis xlim([0 0.08]); %Sets the limits of the x-axis as 0 and 0.08 ylim([0 110]); %Sets the limits of the y-axis as 0 and 110 hold on %Holds all values of t and k end
Flight Path of a Projectile 11 Output: Figure 1: Altitude vs Distance

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Flight Path of a Projectile 12 Figure 2: Altitude vs Time
Flight Path of a Projectile 13 Figure 3: Horizontal Velocity vs Time

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Flight Path of a Projectile 14 Figure 4: Vertical Velocity vs Time
Flight Path of a Projectile 15 Figure 5: Range vs Air Resistance

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Flight Path of a Projectile 16 Figure 6: Total Flight Time vs Air Resistance
Flight Path of a Projectile 17 Discussion By analyzing the graphs obtained from the equations in the theory portion, we can derive several relationships between the time, altitude, range, air resistance, and speed. When we analyze the altitude vs distance graph, we see the expected parabola, with behavior defined by a constant gravitational force and a constant or negligible air resistance. As the value of air resistance increases, both the maximum altitude and maximum range attained decreases. However, range decreases much more quickly as a result of increasing air resistance because that resistance induces drag on the projectile, as shown by the graph. In the altitude vs time graph, we see a similar relationship to the altitude vs distance graph, in both its behavior with increasing values of k and the shape of the graphs. However, the graphs of altitude vs time get longer along the x-axis as opposed to the graphs of altitude vs distance getting shorter along the x-axis as air resistance increases. It reaches its maximum height faster than the time it takes to hit the ground because of the resistance to falling that the friction created by the air provides.

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