In the horizontal velocity vs time graph we see the

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In the horizontal velocity vs time graph, we see the horizontal line sitting at 300 m/s stick out immediately. If there is no air resistance, there is no change in horizontal velocity. Simple physics. The rest of the graphs behave as we would expect. As air resistance increases, the more force there is opposing the direction of motion and velocity of the ball, causing it to slow down at an exponentially increasing rate as the k value increases. In the vertical velocity vs time graph, the graph of v vs t when k =0 agrees with the basic physics we’ve learned over the years in our schooling: with a constant downwards gravitational acceleration, vertical velocity, or velocity in the y direction, decreases at a constant rate. But when air resistance comes into play, it’s behavior changes. For example, the velocity when k = 0.08 decreases much quicker in the first half of its flight time and then levels out to where acceleration is 0. When acceleration is 0, the projectile has reached its terminal velocity and thus cannot accelerate any more. The range and total flight time graphs behave in very much the same way. In other words, as air resistance increases, both the total flight time and range decrease. We can support these results by consulting the previous graphs of y vs x, y vs t, u vs t, and v vs t. The end values of distance on the y vs x graph actually correspond to values plotted on the range graph and the same is true in the case of total flight time and the time on the altitude vs time graph.
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Flight Path of a Projectile 18 One challenge I faced was making sure everything was cooperating correctly. Several times when I tried running the code after a necessary change, I would get errors saying that “These vectors are not equal in size” or “You’re missing something”, etc. For example, in my flightpaths.m function, the time vector was not the same dimension as the other vectors (u,v,x,y,…). So, to fix that, I made the last element in the time vector a blank, e.g.: t(end) = []. Other times I just had to go back a step and compare what worked with what wasn’t working and then error-check the problematic bits. I also had trouble getting the code to create a correct time vector in the flightpaths.m function. To help solve this, I did several trial and error runs, fixing small things every time I tested it. I also consulted Jethro, who helped immensely in figuring out how to make the i- counter work correctly in making the time vector. The biggest challenge I faced, and the one that ultimately got the best of me, was trying to make the range and flight time plot a straight line instead of a whole bunch of dots. I’m not sure exactly what was the problem, but I think it had something to do with the way I was indexing and calculating the vectors for range and flight time and the way they behaved when interacting with the vector k = 0:0.001:0.08. But since it accurately graphed all of the points that would have been on the line, I figured it wasn’t a big deal. I could still accurately analyze the two graphs and what they meant, even if the line wasn’t continuous.
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