Unifrom Free Fall Motion Grapher

In this section you will analyze the results you observed from running the Uniform Free Fall Simulation by plotting the points of distance travelled versus time.

Below is a graph of a the free fall simulation run at a height of 19, and how much time it took to reach the ground, which was 2.0 seconds. As you can see, the curve starts out slowly, with many points close to each other, and then the points start to spread apart from each other and the graph starts moving downwards.

If you would like to see the full code for plotting the time and position graph, click the Display Code button below:

# import required libraries import matplotlib.pyplot as plt import numpy as np def doafit(time,height,order): # initialize layout fig, ax = plt.subplots(figsize = (9,9)) # add scatterplot ax.scatter(time, height, s=60, alpha=0.7, edgecolors="k") params = np.polyfit(time, height, deg=order) ta = np.array(time) xseq = np.linspace(ta.min(), ta.max(), num=100) # plot regression line ff = 0. for i in range(len(params)): ff += params[i]*np.power(xseq,order- i) ax.plot(xseq, ff, color="k", lw=2.5) # axis and title plot labelling ax.set(xlabel="Time", ylabel="Height", title="Uniform Free Fall") ax.grid() return plt # time and height inputs time = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0] height = [19, 18.9, 18.7, 18.4, 18.1, 17.5, 17.0, 16.1, 15.2, 14.3, 13.4, 12.0, 10.8, 9.4, 8.0, 6.3, 4.7, 2.8, 1.0, 0.0] deg = 2 doafit(time, height, deg)

Here is a code editor so that you can input your time and height data points based on your observations made using the Uniform Free Fall simulation.

This is how the time and height inputs should look like:

time = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0]

height = [19, 18.9, 18.7, 18.4, 18.1, 17.5, 17.0, 16.1, 15.2, 14.3, 13.4, 12.0, 10.8, 9.4, 8.0, 6.3, 4.7, 2.8, 1.0, 0.0]

order = 1 means linear fit (i.e. polynomial of degree 1)

order = 2 means quadratic fit (i.e. polynomial of degree 2)

doafit is what generates a fit line or curve based on the time and height inputs.

In the uniform free fall simulation, graph the height and the time. What do you notice in the shape of the curve? is it linear? parabolic?

Do you notice any similarites or differences in your graph compared with the graph above?

Record your observations in the Free Fall worksheet provided in the worksheet section of the Exercises Page.

time = [] height = [] order = 1 doafit(time, height, order )

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