<jupyter_start><jupyter_text>Engineering Recitation Problem 5This problem bothers me on a number of levels but it seems valuable to take the solution and make a plot of the velocity of the rocket as a function of altitude and see what it shows. The numerical calculations are aggravating so it's a perfect place to use python.The problem statement is that the rocket (mass 90,000 kg and constant - not!) has an initial velocity off the launch pad of 100 m/s (too high for sure). The rocket thrust is a constant 2400 kN. Air drag is modelled as $$ F_{drag} = 0.8 v^2 (N)$$The result of the integration after sorting out the freebody diagram is as follows:$$ s = -56250[ln(18.86 - 8.889E-6 v^2) - ln(16.771)]$$If we solve this for v we get...$$ v = \sqrt{\frac{e^{-\frac{s}{56250}+2.819}}{-8.889 \cdot 10^{-6}}} $$<jupyter_code>import numpy as np
import matplotlib.pyplot as plt<jupyter_output><empty_output><jupyter_text>detailss is the altitude which is a linear list of heightsexponent is the exponent of eargument is everything under the square rootTook a couple of tries but it eventually worked.<jupyter_code>altitude = np.linspace(0,700000,100)
exponent = (- altitude/56250.)+2.819
argument = (np.exp(exponent)-16.86)/(-8.889)
speed = np.sqrt(argument)
fig = plt.figure()
ax = plt.axes()
fig.set_size_inches(10, 10)
ax.plot(altitude,speed)<jupyter_output><empty_output>
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