Question

A group of physics students collected data from a test of the projectile motion problem that was analyzed in a previous lab exercise (L5). In their test, the students varied the angle and initial velocity Vo at which the projectile was launched, and then measured the resulting time of flight (tright). Note that tright was the dependent variable, while and Vo were independent variables. The results are listed below. (degrees) Time of Flight (s) Initial Velocity V. (m/s) 15 20 1.71 2.26 2.11 2.81 2.69 3.42 45 60 1.20 1.49 1.85 3.15 3.72 4.45 For the following exercises, work in pairs to solve each problem. Paste your MATLAB code & output in the space beneath each question. Upload the document when finished. 1. Create a MATLAB script file that assigns the data to variables and plots the toon data as a function of V. for = 35 (the first row in the table above). Use symbols not lines for the plot: note that putting a symbol option after any x,y pair causes that data series to be plotted with the specified symbols. For example, plot (x, y, 0) uses circles to plot the x,y data. 2. Next, use one-dimensional (a) linear and (b) spline interpolation to estimate the value of trigne at Vo = 17 and 8 = 35. (Include the MATLAB statements below as well as output.) 3. Create a plot of tight versus Vthat shows 3 sets of markers, one set for each O value. Remember that to plot multiple data series on the same graph, use: plot (x1, y1, x2, y2, ...), where in this particular case x1 and x2 are the same variable V. 4. Now use 2-dimensional interpolation to estimate the value of thigh at V = 22 and = 40.

Answer 1

%4 subparts at a time

Vo=10:5:30;
theta=[35,45,60];
tof=[1.2 1.71 2.26 3.15 3.42;1.49 2.11 2.81 3.72 4.28;1.85 2.69 3.42 4.45 5.24];

%1
figure
plot(Vo,tof(1,:),'*')
xlabel('Initial Velocity Vo (m/s)')
ylabel('Time of Flight (s)')
grid on

%2
linear_output = interp1(Vo,tof(1,:),17);
spline_output = spline(Vo,tof(1,:),17);
fprintf('Tflight calculated using Linear interpolation at Vo = 17 and theta = 35: %f\n',linear_output)
fprintf('Tflight calculated using Spline interpolation at Vo = 17 and theta = 35: %f\n',spline_output)

%3
figure
plot(Vo,tof(1,:),Vo,tof(2,:),Vo,tof(3,:))
legend('\theta = 35','\theta = 45','\theta = 60')
xlabel('Initial Velocity Vo (m/s)')
ylabel('Time of Flight (s)')

%4
interpolated_2d = interp2(Vo,theta,tof,22,40);
fprintf('Tflight calculated using 2d interpolation at Vo = 22 and theta = 40: %f\n',interpolated_2d)

CUIdilu VIHUUW >>> tof_123 Tflight calculated using Linear interpolation at Vo = 17 and theta = 35: 1.930000 Tflight calculated using Spline interpolation at Vo = 17 and theta = 35: 1.890760 Tflight calculated using 2d interpolation at Vo = 22 and theta = 40: 2.895000 - O X - 0 X Figure 1 File Edit View Insert Tools Desktop Window Help DOHOD A O E Figure 2 File Edit View Insert Tools Desktop Window Help DOHODA O E 8 = 35 = 45 = 60 Time of Flight (s) Time of Flight (s) 10 12 14 26 28 30 10 12 14 16 26 28 30 16 18 20 22 24 Initial Velocity Vo (m/s) 18 20 22 24 Initial Velocity Vo (m/s)