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import streamlit as st |
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import numpy as np |
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from abc import ABC, abstractmethod |
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import matplotlib.pyplot as plt |
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class RhinoDisplacement(ABC): |
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@abstractmethod |
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def displacement(self, time): |
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pass |
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class AcceleratingRhino(RhinoDisplacement): |
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def __init__(self, acceleration): |
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self.acceleration = acceleration |
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def displacement(self, time): |
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return 0.5 * self.acceleration * time**2 |
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class ConstantSpeedRhino(RhinoDisplacement): |
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def __init__(self, speed): |
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self.speed = speed |
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def displacement(self, time): |
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return self.speed * time |
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class RhinoMeetingTime(ABC): |
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@abstractmethod |
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def calculate_meeting_time(self, acceleration, speed, distance): |
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pass |
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class CalculateMeetingTime(RhinoMeetingTime): |
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def calculate_meeting_time(self, acceleration, speed, distance): |
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a = 0.5 * acceleration |
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b = speed |
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c = -distance |
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discriminant = b**2 - 4 * a * c |
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if discriminant < 0: |
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return None |
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time = (-b + np.sqrt(discriminant)) / (2 * a) |
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return time |
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class RhinoDisplacementPlot(ABC): |
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@abstractmethod |
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def plot_displacement(self): |
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pass |
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class DisplacementVisualization(RhinoDisplacementPlot): |
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def __init__(self, accelerating_rhino, constant_speed_rhino, meeting_time): |
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self.accelerating_rhino = accelerating_rhino |
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self.constant_speed_rhino = constant_speed_rhino |
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self.meeting_time = meeting_time |
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def plot_displacement(self): |
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fig, ax = plt.subplots() |
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times = np.linspace(0, self.meeting_time, 100) |
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disp_acc = [self.accelerating_rhino.displacement(t) for t in times] |
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disp_const = [self.constant_speed_rhino.displacement(t) for t in times] |
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ax.plot(times, disp_acc, label='Accelerating Rhino') |
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ax.plot(times, disp_const, label='Constant Speed Rhino') |
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ax.annotate('Accelerating rhino = 400 m', (self.meeting_time, disp_acc[-1]), |
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textcoords="offset points", xytext=(-60, 10), ha='center') |
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ax.annotate('Constant speed Rhino = 1200 m', (self.meeting_time, disp_const[-1]), |
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textcoords="offset points", xytext=(-80, -20), ha='center') |
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ax.set_xlabel('Time (s)') |
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ax.set_ylabel('Displacement (m)') |
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ax.legend() |
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return fig |
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def main(): |
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st.title("Rhino Meeting Displacement Calculator") |
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st.image("rhinos_0.png", caption='Rhinos Charging Towards One Another 0') |
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acceleration = 1/8 |
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speed = 15 |
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distance = 1600 |
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if st.button("Generate Rhinos Charging Towards One Another Motion Graph Problem"): |
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st.write("Two rhinos initially 1600 m apart, begin running directly toward one another at the same time. One rhino uniformly accelerates from rest at 1/8 m.s^2, while the other rhino runs with a constant speed of 15 m/s. What is the net displacement of each rhino when they meet?") |
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if st.button("Formulations Required For Solving Problem"): |
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st.write("### Formulations") |
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st.latex(r'AR: s_1(t) = \frac{1}{2}at^2') |
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st.write("") |
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st.latex(r'CSR: s_2(t) = vt') |
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st.write("") |
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st.latex(r'TDCBBR: 1600 meters') |
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st.write("") |
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st.latex(r'Utilize: ax^2 + bx + c = 0') |
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st.write("") |
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st.latex(r'a = \frac{1}{2}\frac{1}{16}t^2') |
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st.write("") |
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st.latex(r'b = 15 m/s') |
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st.write("") |
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st.latex(r'\frac{1}{16}t^2 + 15t = 1600') |
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st.write("") |
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st.latex(r'c= -1600') |
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st.write("") |
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st.latex(r'\Delta = b^2 - 4ac = 15^2 - 4\frac{1}{16}1600 = 225 + 400 = 625') |
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st.write("") |
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st.latex(r'Solve: t = \frac{-15+-\sqrt(625)}{\frac{1}{8}} = \frac{-15 +- 25}{\frac{1}{8}}') |
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st.write("") |
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st.latex(r'Psol: t = \frac{10}{\frac{1}{8}} = 80 seconds') |
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st.write("") |
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st.latex(r's_1(t) = s_1(80) = \frac{1}{2}\frac{1}{8}80^2 = \frac{1}{16}6400 = 400 meters') |
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st.write("") |
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st.latex(r's_2(t) = s_2(80) = 15 * 80 = 1200 meters') |
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st.write("") |
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if st.button("Calculate"): |
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calc_meeting_time = CalculateMeetingTime() |
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time = calc_meeting_time.calculate_meeting_time(acceleration, speed, distance) |
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if time is not None: |
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accelerating_rhino = AcceleratingRhino(acceleration) |
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constant_speed_rhino = ConstantSpeedRhino(speed) |
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disp_acc = accelerating_rhino.displacement(time) |
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disp_const = constant_speed_rhino.displacement(time) |
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st.write(f"Time to meet: {time:.2f} seconds") |
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st.write(f"Displacement of accelerating rhino: {disp_acc:.2f} meters") |
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st.write(f"Displacement of constant speed rhino: {disp_const:.2f} meters") |
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visualization = DisplacementVisualization(accelerating_rhino, constant_speed_rhino, time) |
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fig = visualization.plot_displacement() |
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st.pyplot(fig) |
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else: |
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st.write("The rhinos will never meet under these conditions.") |
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st.image("rhinos_1.png", caption='Rhinos Charging Towards One Another 1') |
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if __name__ == "__main__": |
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main() |