Week 3

8th-Semester-Spring-2025/biology/week-3/Sharpe_VocabularyAssignment3.md

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+---
+title: Vocabulary Assignment 3
+author: Aidan Sharpe
+date: February 20th, 2025
+geometry: margin=1in
+---
+
+
+## Atoms
+An atom is the smallest elemental particle that retains it's chemical properties.
+
+## Molecules
+Two or more atoms chemically bonded, creating a new material with unique chemical properties. 
+
+## Organelles
+Functional structures within biological cells.
+
+## Cells
+The smallest functional unit of life.
+
+## Tissues
+A structure comprised of cells of the same type that performs a specific function.
+
+## Organs
+A structure comprised of tissues that fulfill a task within an organ system.
+
+## Organ systems
+A collection of organs that perform a similar task.
+
+## Body membranes
+A biological barrier that lines organs and cavities.
+
+## Interstitial fluids
+Bodily fluids that exist between, as opposed to within, cells.
+
+## Homeostasis
+The tendency for living organisms to maintain a stable internal environment.

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q2.m

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+% Lab 2
+% Question 2 on periodicity
+
+% Define the samples axis (0 to 50, including 50)
+n=0:1:50;
+
+% Define four cosines at different frequencies
+x1=cos(2*pi*n/7);
+x2=cos(2*pi*n/21);
+x3=cos(2*pi*n/17.5);
+x4=cos(2*n/7);
+
+% Plot each of the cosines in a separate subplot
+subplot(411)
+stem(n,x1,'linewidth',2)
+subplot(412)
+stem(n,x2,'linewidth',2)
+subplot(413)
+stem(n,x3,'linewidth',2)
+subplot(414)
+stem(n,x4,'linewidth',2)
+xlabel('n');
+

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q2.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+def main():
+    # Define the samples axis (0 to 51, excluding 51)
+    n = np.arange(51)
+    
+    # Define the four frequencies used
+    f_1 = 1/7
+    f_2 = 1/21
+    f_3 = 1/17.5
+    f_4 = 1/(7*np.pi)
+
+    # Convert frequencies to angular frequency
+    omega_1 = 2*np.pi*f_1
+    omega_2 = 2*np.pi*f_2
+    omega_3 = 2*np.pi*f_3
+    omega_4 = 2*np.pi*f_4
+
+    # Sample a cosine of each of the 
+    x_1 = np.cos(omega_1*n)
+    x_2 = np.cos(omega_2*n)
+    x_3 = np.cos(omega_3*n)
+    x_4 = np.cos(omega_4*n)
+    
+    # Plot each of the cosines in a separate subplot
+    plt.subplot(411)
+    plt.stem(n, x_1)
+
+    plt.subplot(412)
+    plt.stem(n, x_2)
+
+    plt.subplot(413)
+    plt.stem(n, x_3)
+
+    plt.subplot(414)
+    plt.stem(n, x_4)
+    plt.xlabel("n")
+
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q3.m

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+clear x
+n=0:1:12;
+x(n+1)=0;
+x(6)=1;
+x(9)=-2;
+x(12)=6;
+figure(1)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');
+
+clear x
+n=0:1:15;
+x(n+1)=0;
+for m=0:15
+    if (m < 3)
+        x(m+1) = 0;
+    elseif (m >=3 && m < 8)
+        x(m+1)  = 1;
+    elseif (m >= 8 && m < 12)
+        x(m+1) = -1;
+    end
+end
+figure(2)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');
+
+clear x
+n=0:1:20;
+x(n+1)=n;
+figure(3)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');
+
+clear x
+n=0:1:10;
+x(1)=0;
+for m=1:10
+    x(m+1)=m*m;
+end
+figure(4)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');
+
+clear x
+n=0:1:30;
+for m=0:30
+    x(m+1)=3*(m-3)*(m-3)*exp(-0.3*m)*sin(2*m/3);
+end
+figure(5)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q3.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def delta(n):
+    return np.where(n==0, 1, 0)
+
+
+def u(n):
+    return np.heaviside(n, 1)
+
+
+def main():
+    # Part a
+    n = np.arange(13)
+    x = delta(n-5) - 2*delta(n-8) + 6*delta(n-11)
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel(r"$x[n] = \delta(n-5) - 2\delta(n-8) + 6\delta(n-11)$")
+    plt.show()
+
+    # Part b
+    n = np.arange(16)
+    x = u(n-3) - 2*u(n-8) + u(n-12)
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel("$x[n] = u(n-3) - 2u(n-8) + u(n-12)$")
+    plt.show()
+
+    # Part c
+    n = np.arange(21)
+    x = n*u(n)
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel("$x[n] = n u(n)$")
+    plt.show()
+
+    # Part d
+    n = np.arange(11)
+    x = n**2 * u(n)
+    plt.stem(n, x)
+    plt.xlabel(r"$n$")
+    plt.ylabel(r"$x[n] = n^2 u(n)$")
+    plt.show()
+
+    # Part e
+    n = np.arange(31)
+    x = 3 * (n-3)**2 * np.exp(-0.3*n) * np.sin(2*n/3) * u(n)
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel(r"$x[n] = 3(n-3)^2 e^{-0.3n} \sin(2n/3) u(n)$")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q4.m

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+clear x
+a=pi/4;
+n=0:1:50;
+x(n+1)=5*cos(a*a*n);
+figure(1)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');
+
+clear x
+a=5;
+c=abs(0.5+0.5*j);
+n=0:1:50;
+for m=0:50
+    x(m+1)=a*c^m;
+end
+figure(2)
+stem(n,x,'linewidth',2)
+xlabel('n');
+ylabel('x(n)');

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q4.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def u(n):
+    return np.heaviside(n, 1)
+
+
+def main():
+    # Part a
+    a = np.pi/4
+    n = np.arange(51)
+    x = 5*np.cos(a**2 * n)
+
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel(r"$x[n] = 5\cos(a^2 n)$")
+    plt.show()
+
+    # Part b
+    A = 5
+    b = (1 + 1j)/2
+    x = A*np.abs(b)**n * u(n)
+
+    plt.stem(n, x)
+    plt.xlabel("$n$")
+    plt.ylabel("$x[n] = A|b|^n u(n)$")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q5.m

@@ -0,0 +1,10 @@
+energy(1)=1;
+for k=2:500
+    energy(k)=energy(k-1) + (1/(k*k));
+end
+a=(pi*pi/6)*ones(length(energy),1);
+plot(energy,'linewidth',2)
+hold
+plot(a,'r','linewidth',2)
+xlabel('Time index');
+ylabel('Energy');

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q5.py

@@ -0,0 +1,26 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def u(n):
+    return np.heaviside(n, 1)
+
+
+def main():
+    n = np.arange(101)
+    x = u(n-1)/n
+
+    # Avoid divide by zero
+    x[0] = 0
+    # Calculate the energy as a cumulative sum from n=0 to each sample
+    energy = np.cumsum(np.abs(x)**2)
+
+    plt.stem(n, energy)
+    plt.hlines(np.pi**2 / 6, n[0], n[-1], color='r')
+    plt.xlabel("Time index")
+    plt.ylabel("Energy")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q6.m

@@ -0,0 +1,30 @@
+n=0:1:6;
+x=[1 -5 4 -8 6 -3 -1];
+figure(1)
+stem(n,x,'linewidth',2)
+xlabel('Time index');
+ylabel('x(n)');
+
+for m=0:6
+    u=mod(m+3,7);
+    y1(m+1)=x(u+1);
+    u=mod(m-4,7);
+    y2(m+1)=x(u+1);
+    u=mod(-m+2,7);
+    y3(m+1)=x(u+1);
+end
+
+figure(2)
+stem(n,y1,'linewidth',2)
+xlabel('Time index');
+ylabel('x(n+3 mod 7)');
+
+figure(3)
+stem(n,y2,'linewidth',2)
+xlabel('Time index');
+ylabel('x(n-4 mod 7)');
+
+figure(4)
+stem(n,y3,'linewidth',2)
+xlabel('Time index');
+ylabel('x(-n+2 mod 7)');

8th-Semester-Spring-2025/clinic-consultant/labs/lab-2/lab2q6.py

@@ -0,0 +1,35 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def main():
+    n = np.arange(7)        # n ranges from 0 to 7 (not including 7)
+    x = np.array([1, -5, 4, -8, 6, -3, -1])
+
+    x_1 = x[(n+3) % 7]      # x[ <n+3>_7 ]
+    x_2 = x[(n-4) % 7]      # x[ <n-4>_7 ]
+    x_3 = x[(-n+2) % 7]     # x[ <-n+2>_7 ]
+
+    plt.subplot(411)
+    plt.stem(n,x)
+    plt.ylabel("$x[n]$")
+
+    plt.subplot(412)
+    plt.stem(n,x_1)
+    plt.ylabel(r"$x[\langle n+3 \rangle_7]$")
+
+    plt.subplot(413)
+    plt.stem(n, x_2)
+    plt.ylabel(r"$x[\langle n-4\rangle_7]$")
+
+    plt.subplot(414)
+    plt.stem(n, x_3)
+    plt.ylabel(r"$x[\langle -n+2\rangle_7]$")
+
+    plt.xlabel("$n$")
+    plt.show()
+
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/cloud-hardware/Project 2-2/Project 2-2.pem

@@ -0,0 +1,27 @@
+-----BEGIN RSA PRIVATE KEY-----
+MIIEowIBAAKCAQEAwBCAWsvUNRP+Ar36WVT3eHR67OpHFewp67i1MKu9AKrd6HBL
+wEbzcIK7yijJCNnqMmLhBtfV3olD1bEG2hEBdj8UujE23vk8zXCYf7SVuBZ4NX3+
+gYVtGZlKSlmWpes245dslXtnOLvrxdtLh2ixZB7fDfNeO/I77VY2F0jzDdo3D6Wv
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+qbiRvpW5yR12QUh/dh7jYe0yvePGSFdDoS124wIDAQABAoIBAEzhDg/KERph80Yz
+t1c0vI45yc61hFjRHIKff9+IjvIKcyMMeDXx8JXzrqmgI8BoQeeDTuHHWXNnbIDI
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+GLyN+pvCA7T42pqSPsykuqgdajT7l42D4rUWzfI3mEeMMwvZwfVIaEtWR3TEJ+zW
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+jbHrSuZG+zRW/CH25geCUU1HzHR6WD7pfMBu+mshoCMZl5cRlq0Nu5RbbnnnFqy3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+-----END RSA PRIVATE KEY-----

8th-Semester-Spring-2025/cloud-hardware/Questions 1-10/questions-1-10.md

@@ -0,0 +1,16 @@
+---
+title: Cloud Hardware Questions 1-10
+author: Aidan Sharpe
+date: Thursday, Feb 13th, 2025
+---
+
+1. b. Measured service
+2. b. SaaS
+3. b. Minimal cost
+4. d. Orchestration
+5. c. SLA
+6. d. Resource pooling
+7. b. SOC 2
+8. d. API
+9. b. Storage and c. Compute
+10. b. While identifying the problem

8th-Semester-Spring-2025/pcb-design/protoboarding/protoboarding.md

@@ -23,6 +23,21 @@ This exercise transitions the breadboarded circuit from the last exercise to a p
 
 The goal of the completed board is to have a common ground pin and individual power pins for each LEDs. This allows for independent control of the LEDs. The components are all to be permanently affixed to the protoboard with solder. In doing so, our prototype will be more durable than a simple breadboard layout.
 
+## Requirements
+1. Traffic light LEDs
+	1. Traffic light shall have three (3) LEDs
+	2. The top LED (furthest from pin header) shall be red
+	3. The middle LED shall be yellow
+	4. The bottom LED (closest to pin header) shall be green
+	5. All LEDs shall have a 220$\Omega$ resistor connected in series to the power connection
+2. Traffic light header
+	1. Header shall be 1 row, 6 positions, male (pins), 90-degree, through-hole mount, 100 mil pitch
+	2. Header shall be extend from the short side of the board
+	3. Pin 0 shall be a common ground pin
+	4. Pin 1 shall supply +5V to the red LED
+	5. Pin 2 shall supply +5V to the yellow LED
+	6. Pin 3 shall supply +5V to the green LED
+
 ## Procedure
 First, we had to modify the protoboard and the pin header for them to mate properly. Since we are using stripboard as opposed to perfboard [@MorePCB], some of the pins would be shorted together through the pre-existing traces. We also had to remove two pins from the pin header, because the pins do not have a corresponding hole on the board.
 

8th-Semester-Spring-2025/weapon-systems/homework/C_N_alpha.py

@@ -0,0 +1,19 @@
+import numpy as np
+import atmospheric_model as atmos
+
+M = 400
+D = 0.1
+alpha = np.radians(40)
+g = 9.81
+a = 30*g
+alt = 5000
+v = 600
+
+N = M*a
+S_ref = np.pi * (D/2)**2
+Q = atmos.dynamic_pressure(alt, v)
+
+C_N = N/(Q*S_ref)
+C_N_alpha = C_N/alpha
+
+print(C_N_alpha)

8th-Semester-Spring-2025/weapon-systems/homework/atmospheric_model.py

@@ -0,0 +1,43 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def temperature(altitude):
+    if altitude > 25000:
+        return -131.21 + 0.00299*altitude
+    elif altitude > 11000:
+        return -56.46
+    else:
+        return 15.04 - 0.00649*altitude
+
+
+def pressure(altitude):
+    T = temperature(altitude)
+    if altitude > 25000:
+        kpa = 2.488 * ((T+273.1)/216.6)**(-11.388)
+    elif altitude > 11000:
+        kpa = 22.65 * np.exp(1.73 - 0.000157*alititude)
+    else:
+        kpa = 101.29 * ((T+273.1)/288.08)**5.256
+    return 1000*kpa
+
+def atmospheric_density(altitude):
+    p = pressure(altitude)
+    T = temperature(altitude)
+    return p / (286.9*(T+273.1))
+
+
+def Mach(altitude, speed):
+    return speed/speed_of_sound(altitude)
+
+
+def speed_of_sound(altitude):
+    gamma = 1.4
+    p = pressure(altitude)
+    rho = atmospheric_density(altitude)
+    return (gamma*p/rho)**0.5
+
+
+def dynamic_pressure(altitude, speed):
+    rho = atmospheric_density(altitude)
+    return rho * speed**2 / 2

8th-Semester-Spring-2025/weapon-systems/homework/axial_drag.py

@@ -0,0 +1,20 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def CA(Mach):
+    return np.where(Mach > 1.0, 0.02 + 0.03/Mach,
+           np.where(Mach > 0.5, 0.02*(Mach-0.5) + 0.04, 0.04))
+
+
+def main():
+    Mach = np.linspace(0,5,100)
+    plt.plot(Mach, CA(Mach))
+    plt.xlabel("Mach number")
+    plt.ylabel("CA")
+    plt.savefig("axial_drag.png")
+    plt.show()
+
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/weapon-systems/homework/cannonball.py

@@ -0,0 +1,125 @@
+import atmospheric_model as atmos
+import axial_drag
+import numpy as np
+import matplotlib.pyplot as plt
+
+IGNORE_AIR_RESISTANCE = False
+
+g = -9.81
+v_initial = 600
+S_ref = 0.1
+mass = 10
+T_s = 0.05
+
+def main():
+    plt.figure(figsize=(16,9))
+    for elevation in np.arange(10,81,10):
+        theta = np.radians(elevation)
+        v_x = v_initial * np.cos(theta)
+        v_y = v_initial * np.sin(theta)
+        a_x = 0
+        a_y = g
+
+        t = 0
+        x = 0
+        y = 0
+
+        x_values = []
+        y_values = []
+        x_velocities = []
+        y_velocities = []
+        x_accelerations = []
+        y_accelerations = []
+        time = []
+
+        while y >= 0:
+            t += T_s
+
+            if not IGNORE_AIR_RESISTANCE:
+                v = (v_x*v_x + v_y*v_y)**0.5
+
+                Mach = atmos.Mach(y, v)
+                CA = axial_drag.CA(Mach)
+                Q = atmos.dynamic_pressure(y, v)
+                drag = CA*Q*S_ref
+                
+                angle = np.arctan(v_y/v_x) + np.pi
+                drag_x = drag*np.cos(angle)
+                drag_y = drag*np.sin(angle)
+
+                a_x = drag_x/mass
+                a_y = drag_y/mass + g
+
+            x_accelerations.append(a_x)
+            y_accelerations.append(a_y)
+
+            x += v_x*T_s
+            x_values.append(x)
+            y += v_y*T_s
+            y_values.append(y)
+
+            v_x += a_x*T_s
+            x_velocities.append(v_x)
+            v_y += a_y*T_s
+            y_velocities.append(v_y)
+
+            time.append(t)
+
+        x_pos = np.array(x_values)/1000
+        y_pos = np.array(y_values)/1000
+        distance = (x_pos*x_pos + y_pos*y_pos)**0.5
+
+        v_x = np.array(x_velocities)
+        v_y = np.array(y_velocities)
+        speed = (v_x*v_x + v_y*v_y)**0.5
+
+        a_x = np.array(x_accelerations)/9.81
+        a_y = np.array(y_accelerations)/9.81
+        acceleration = (a_x*a_x + a_y*a_y)**0.5
+
+        plt.subplot(331)
+        plt.plot(time, x_pos)
+        plt.ylabel("Horizontal position [km]")
+
+        plt.subplot(332)
+        plt.plot(time, y_pos)
+        plt.ylabel("Vertical position [km]")
+
+        plt.subplot(333)
+        plt.plot(time, distance)
+        plt.ylabel("Total distance [km]")
+
+        plt.subplot(334)
+        plt.plot(time, v_x)
+        plt.ylabel("Horizontal velocity [m/s]")
+
+        plt.subplot(335)
+        plt.plot(time, v_y)
+        plt.ylabel("Vertical velocity [m/s]")
+
+        plt.subplot(336)
+        plt.plot(time, speed)
+        plt.ylabel("Speed [m/s]")
+
+        plt.subplot(337)
+        plt.plot(time, a_x)
+        plt.ylabel("Horizontal acceleration [g]")
+        plt.xlabel("Time [s]")
+
+        plt.subplot(338)
+        plt.plot(time, a_y)
+        plt.ylabel("Vertical acceleration [g]")
+        plt.xlabel("Time [s]")
+
+        plt.subplot(339)
+        plt.plot(time, acceleration)
+        plt.ylabel("Total acceleration [g]")
+        plt.xlabel("Time [s]")
+
+    
+    plt.savefig("cannonball.png")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()

8th-Semester-Spring-2025/weapon-systems/homework/homework1.md

@@ -0,0 +1,233 @@
+---
+title: Homework 1
+author: Aidan Sharpe
+date: February 10th, 2025
+geometry: margin=1in
+output:
+	pdf_document:
+		md_extension: native_numbering
+---
+
+# Develop an Atmospheric Model
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def temperature(altitude):
+    if altitude > 25000:
+        return -131.21 + 0.00299*altitude
+    elif altitude > 11000:
+        return -56.46
+    else:
+        return 15.04 - 0.00649*altitude
+
+
+def pressure(altitude):
+    T = temperature(altitude)
+    if altitude > 25000:
+        kpa = 2.488 * ((T+273.1)/216.6)**(-11.388)
+    elif altitude > 11000:
+        kpa = 22.65 * np.exp(1.73 - 0.000157*alititude)
+    else:
+        kpa = 101.29 * ((T+273.1)/288.08)**5.256
+    return 1000*kpa
+
+def atmospheric_density(altitude):
+    p = pressure(altitude)
+    T = temperature(altitude)
+    return p / (286.9*(T+273.1))
+
+
+def Mach(altitude, speed):
+    return speed/speed_of_sound(altitude)
+
+
+def speed_of_sound(altitude):
+    gamma = 1.4
+    p = pressure(altitude)
+    rho = atmospheric_density(altitude)
+    return (gamma*p/rho)**0.5
+
+
+def dynamic_pressure(altitude, speed):
+    rho = atmospheric_density(altitude)
+    return rho * speed**2 / 2
+```
+
+# Determining $C_{N_\alpha}$
+```python
+import numpy as np
+import atmospheric_model as atmos
+
+M = 400
+D = 0.1
+alpha = np.radians(40)
+g = 9.81
+a = 30*g
+alt = 5000
+v = 600
+
+N = M*a
+S_ref = np.pi * (D/2)**2
+Q = atmos.dynamic_pressure(alt, v)
+
+C_N = N/(Q*S_ref)
+C_N_alpha = C_N/alpha
+
+print(C_N_alpha)
+```
+
+$C_{N_\alpha} = 161.69$
+
+# Develop an Axial Drag Model
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+def CA(Mach):
+    return np.where(Mach > 1.0, 0.02 + 0.03/Mach,
+           np.where(Mach > 0.5, 0.02*(Mach-0.5) + 0.04, 0.04))
+
+
+def main():
+    Mach = np.linspace(0,5,100)
+	plt.savefig("axial_drag.png")
+    plt.plot(Mach, CA(Mach))
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()
+```
+
+![](axial_drag.png)
+
+# Cannonball
+```python
+import atmospheric_model as atmos
+import axial_drag
+import numpy as np
+import matplotlib.pyplot as plt
+
+IGNORE_AIR_RESISTANCE = False
+
+g = -9.81
+v_initial = 600
+S_ref = 0.1
+mass = 10
+T_s = 0.05
+
+def main():
+    for elevation in np.arange(10,81,10):
+        theta = np.radians(elevation)
+        v_x = v_initial * np.cos(theta)
+        v_y = v_initial * np.sin(theta)
+        a_x = 0
+        a_y = g
+
+        t = 0
+        x = 0
+        y = 0
+
+        x_values = []
+        y_values = []
+        x_velocities = []
+        y_velocities = []
+        x_accelerations = []
+        y_accelerations = []
+        time = []
+
+        while y >= 0:
+            t += T_s
+
+            if not IGNORE_AIR_RESISTANCE:
+                v = (v_x*v_x + v_y*v_y)**0.5
+
+                Mach = atmos.Mach(y, v)
+                CA = axial_drag.CA(Mach)
+                Q = atmos.dynamic_pressure(y, v)
+                drag = CA*Q*S_ref
+                
+                angle = np.arctan(v_y/v_x) + np.pi
+                drag_x = drag*np.cos(angle)
+                drag_y = drag*np.sin(angle)
+
+                a_x = drag_x/mass
+                a_y = drag_y/mass + g
+
+            x_accelerations.append(a_x)
+            y_accelerations.append(a_y)
+
+            x += v_x*T_s
+            x_values.append(x)
+            y += v_y*T_s
+            y_values.append(y)
+
+            v_x += a_x*T_s
+            x_velocities.append(v_x)
+            v_y += a_y*T_s
+            y_velocities.append(v_y)
+
+            time.append(t)
+
+        x_pos = np.array(x_values)/1000
+        y_pos = np.array(y_values)/1000
+        distance = (x_pos*x_pos + y_pos*y_pos)**0.5
+
+        v_x = np.array(x_velocities)
+        v_y = np.array(y_velocities)
+        speed = (v_x*v_x + v_y*v_y)**0.5
+
+        a_x = np.array(x_accelerations)/9.81
+        a_y = np.array(y_accelerations)/9.81
+        acceleration = (a_x*a_x + a_y*a_y)**0.5
+
+        plt.subplot(331)
+        plt.plot(time, x_pos)
+        plt.ylabel("Horizontal position [km]")
+
+        plt.subplot(332)
+        plt.plot(time, y_pos)
+        plt.ylabel("Vertical position [km]")
+
+        plt.subplot(333)
+        plt.plot(time, distance)
+        plt.ylabel("Total distance [km]")
+
+        plt.subplot(334)
+        plt.plot(time, v_x)
+        plt.ylabel("Horizontal velocity [m/s]")
+
+        plt.subplot(335)
+        plt.plot(time, v_y)
+        plt.ylabel("Vertical velocity [m/s]")
+
+        plt.subplot(336)
+        plt.plot(time, speed)
+        plt.ylabel("Speed [m/s]")
+
+        plt.subplot(337)
+        plt.plot(time, a_x)
+        plt.ylabel("Horizontal acceleration [g]")
+        plt.xlabel("Time [s]")
+
+        plt.subplot(338)
+        plt.plot(time, a_y)
+        plt.ylabel("Vertical acceleration [g]")
+        plt.xlabel("Time [s]")
+
+        plt.subplot(339)
+        plt.plot(time, acceleration)
+        plt.ylabel("Total acceleration [g]")
+        plt.xlabel("Time [s]")
+
+    plt.savefig("cannonball.png")
+    plt.show()
+
+
+if __name__ == "__main__":
+    main()
+```
+
+![](cannonball.png)