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import matplotlib.pyplot as plt
from vector_physics import Vector2D, VectorPhysicsSimulator, plot_vectors, plot_trajectory, UnitConverter, QuizGenerator
# Configure Streamlit
st.set_page_config(page_title="Vector Physics Tutorial", layout="wide")
# Initialize simulator and quiz generator
simulator = VectorPhysicsSimulator()
quiz_gen = QuizGenerator()
converter = UnitConverter()
# Initialize session state
if 'quiz_question' not in st.session_state:
st.session_state.quiz_question = None
if 'quiz_answer' not in st.session_state:
st.session_state.quiz_answer = None
if 'quiz_submitted' not in st.session_state:
st.session_state.quiz_submitted = False
if 'show_explanation' not in st.session_state:
st.session_state.show_explanation = False
# Title and introduction
st.title("🚢 Vector Physics Interactive Tutorial")
st.markdown("""
Welcome to the Vector Physics Tutorial! Vectors are quantities that have both magnitude and direction.
Use the controls below to explore different vector scenarios and see how they behave in real-time.
""")
# Sidebar for navigation
st.sidebar.title("Select Physics Problem")
problem_type = st.sidebar.selectbox(
"Choose a problem type:",
["Boat Crossing", "Projectile Motion", "Vector Addition", "Quiz Mode"]
)
# Unit selection
st.sidebar.markdown("---")
st.sidebar.subheader("🔧 Unit Settings")
speed_unit = st.sidebar.selectbox("Speed Units:", list(converter.speed_conversions().keys()))
distance_unit = st.sidebar.selectbox("Distance Units:", list(converter.distance_conversions().keys()))
# Reset button
if st.sidebar.button("🔄 Reset to Defaults", help="Reset all controls to default values"):
st.rerun()
if problem_type == "Boat Crossing":
st.header("🚢 Boat Crossing a River")
st.markdown("""
A boat is trying to cross a river with a current. The boat has its own velocity,
and the river current affects the boat's actual path.
""")
col1, col2 = st.columns([1, 2])
with col1:
st.subheader("Controls")
# Convert default values to selected units
default_boat_speed = converter.convert_speed(5.0, "m/s", speed_unit)
default_current_speed = converter.convert_speed(3.0, "m/s", speed_unit)
boat_speed_input = st.slider(f"Boat Speed ({speed_unit})", 0.1,
converter.convert_speed(10.0, "m/s", speed_unit),
default_boat_speed, 0.1)
boat_angle = st.slider("Boat Direction (degrees)", -90, 90, 45, 1)
current_speed_input = st.slider(f"Current Speed ({speed_unit})", 0.0,
converter.convert_speed(8.0, "m/s", speed_unit),
default_current_speed, 0.1)
current_angle = st.slider("Current Direction (degrees)", -180, 180, 180, 1)
# Convert back to m/s for calculations
boat_speed = converter.convert_speed(boat_speed_input, speed_unit, "m/s")
current_speed = converter.convert_speed(current_speed_input, speed_unit, "m/s")
# Calculate results
results = simulator.boat_crossing_problem(boat_speed, boat_angle, current_speed, current_angle)
st.subheader("Results")
st.write(f"**Boat Velocity:** {converter.convert_speed(results['boat_velocity'].magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {results['boat_velocity'].angle:.1f}°")
st.write(f"**Current Velocity:** {converter.convert_speed(results['current_velocity'].magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {results['current_velocity'].angle:.1f}°")
st.write(f"**Resultant Velocity:** {converter.convert_speed(results['resultant_velocity'].magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {results['resultant_velocity'].angle:.1f}°")
# Show heading difference
st.markdown("---")
st.subheader("📐 Navigation Analysis")
st.write(f"**Heading Difference:** {results['heading_difference']:.1f}°")
if results['heading_difference'] > 10:
st.warning(f"⚠️ The boat's actual path deviates {results['heading_difference']:.1f}° from intended direction!")
else:
st.success("✅ The boat is following close to its intended path.")
with col2:
# Create plots
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
# Vector diagram
vectors = [results['boat_velocity'], results['current_velocity'], results['resultant_velocity']]
labels = ['Boat Velocity (intended)', 'Current Velocity', 'Resultant Velocity (actual)']
colors = ['blue', 'red', 'green']
plot_vectors(ax1, vectors, labels, colors)
ax1.set_title("Vector Diagram")
# Trajectory plot
traj_x_converted = [converter.convert_distance(x, "meters", distance_unit) for x in results['trajectory_x'][:50]]
traj_y_converted = [converter.convert_distance(y, "meters", distance_unit) for y in results['trajectory_y'][:50]]
plot_trajectory(ax2, traj_x_converted, traj_y_converted, f"Boat Path ({distance_unit})")
ax2.set_xlabel(f'X Position ({distance_unit})')
ax2.set_ylabel(f'Y Position ({distance_unit})')
st.pyplot(fig)
elif problem_type == "Projectile Motion":
st.header("🎯 Projectile Motion")
st.markdown("""
A projectile is launched at an angle. Gravity acts downward while the horizontal
component of velocity remains constant. **Error analysis** shows how measurement
uncertainty affects the results.
""")
col1, col2 = st.columns([1, 2])
with col1:
st.subheader("Controls")
default_speed = converter.convert_speed(20.0, "m/s", speed_unit)
initial_speed_input = st.slider(f"Initial Speed ({speed_unit})", 1.0,
converter.convert_speed(50.0, "m/s", speed_unit),
default_speed, 1.0)
launch_angle = st.slider("Launch Angle (degrees)", 0, 90, 45, 1)
gravity = st.slider("Gravity (m/s²)", 1.0, 15.0, 9.81, 0.1)
show_error = st.checkbox("Show Error Analysis", value=True, help="Shows uncertainty range from measurement errors")
# Convert to m/s for calculations
initial_speed = converter.convert_speed(initial_speed_input, speed_unit, "m/s")
# Calculate results
results = simulator.projectile_motion(initial_speed, launch_angle, gravity)
st.subheader("Results")
st.write(f"**Initial Velocity:** {converter.convert_speed(results['initial_velocity'].magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {results['initial_velocity'].angle:.1f}°")
st.write(f"**Max Range:** {converter.convert_distance(results['max_range'], 'meters', distance_unit):.2f} {distance_unit}")
st.write(f"**Max Height:** {converter.convert_distance(results['max_height'], 'meters', distance_unit):.2f} {distance_unit}")
st.write(f"**Flight Time:** {results['time_points'][-1]:.2f} s")
if show_error:
st.markdown("---")
st.subheader("📊 Uncertainty Analysis")
st.write(f"**Speed Uncertainty:** ±{converter.convert_speed(results['speed_uncertainty'], 'm/s', speed_unit):.2f} {speed_unit}")
st.write(f"**Angle Uncertainty:** ±{results['angle_uncertainty']:.1f}°")
st.info("💡 Small measurement errors can lead to significant differences in trajectory!")
with col2:
# Create plots
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
# Vector diagram
initial_vel = results['initial_velocity']
velocity_x = Vector2D(initial_vel.x, 0)
velocity_y = Vector2D(0, initial_vel.y)
vectors = [velocity_x, velocity_y, initial_vel]
labels = ['Horizontal Component', 'Vertical Component', 'Initial Velocity']
colors = ['blue', 'red', 'green']
plot_vectors(ax1, vectors, labels, colors)
ax1.set_title("Velocity Components")
# Trajectory plot with error analysis
traj_x = [converter.convert_distance(x, "meters", distance_unit) for x in results['trajectory_x']]
traj_y = [converter.convert_distance(y, "meters", distance_unit) for y in results['trajectory_y']]
error_bounds = None
if show_error:
error_bounds = {
'upper_x': [converter.convert_distance(x, "meters", distance_unit) for x in results['error_upper_x']],
'upper_y': [converter.convert_distance(y, "meters", distance_unit) for y in results['error_upper_y']],
'lower_x': [converter.convert_distance(x, "meters", distance_unit) for x in results['error_lower_x']],
'lower_y': [converter.convert_distance(y, "meters", distance_unit) for y in results['error_lower_y']]
}
plot_trajectory(ax2, traj_x, traj_y, f"Projectile Path ({distance_unit})", error_bounds)
ax2.set_xlabel(f'X Position ({distance_unit})')
ax2.set_ylabel(f'Y Position ({distance_unit})')
st.pyplot(fig)
elif problem_type == "Vector Addition":
st.header("➕ Vector Addition Practice")
st.markdown("""
Practice adding vectors by adjusting their magnitudes and directions.
See how different combinations create different resultant vectors.
""")
col1, col2 = st.columns([1, 2])
with col1:
st.subheader("Vector A")
default_mag_a = converter.convert_speed(5.0, "m/s", speed_unit)
mag_a_input = st.slider(f"Magnitude A ({speed_unit})", 0.1,
converter.convert_speed(10.0, "m/s", speed_unit),
default_mag_a, 0.1, key="mag_a")
angle_a = st.slider("Angle A (degrees)", -180, 180, 30, 1, key="angle_a")
st.subheader("Vector B")
default_mag_b = converter.convert_speed(3.0, "m/s", speed_unit)
mag_b_input = st.slider(f"Magnitude B ({speed_unit})", 0.1,
converter.convert_speed(10.0, "m/s", speed_unit),
default_mag_b, 0.1, key="mag_b")
angle_b = st.slider("Angle B (degrees)", -180, 180, 120, 1, key="angle_b")
# Convert to m/s for calculations
mag_a = converter.convert_speed(mag_a_input, speed_unit, "m/s")
mag_b = converter.convert_speed(mag_b_input, speed_unit, "m/s")
# Create vectors
vector_a = Vector2D(magnitude=mag_a, angle=angle_a)
vector_b = Vector2D(magnitude=mag_b, angle=angle_b)
resultant = vector_a + vector_b
st.subheader("Results")
st.write(f"**Vector A:** {converter.convert_speed(vector_a.magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {vector_a.angle:.1f}°")
st.write(f"**Vector B:** {converter.convert_speed(vector_b.magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {vector_b.angle:.1f}°")
st.write(f"**Resultant:** {converter.convert_speed(resultant.magnitude, 'm/s', speed_unit):.2f} {speed_unit} at {resultant.angle:.1f}°")
st.write(f"**Dot Product A·B:** {vector_a.dot_product(vector_b):.2f}")
st.write(f"**Angle Between Vectors:** {vector_a.angle_between(vector_b):.1f}°")
with col2:
fig, ax = plt.subplots(figsize=(8, 8))
vectors = [vector_a, vector_b, resultant]
labels = ['Vector A', 'Vector B', 'Resultant A+B']
colors = ['blue', 'red', 'green']
plot_vectors(ax, vectors, labels, colors)
ax.set_title("Vector Addition")
st.pyplot(fig)
elif problem_type == "Quiz Mode":
st.header("🎓 Vector Physics Quiz")
st.markdown("""
Test your understanding of vector concepts! Click 'New Question' to get a random problem.
""")
col1, col2, col3 = st.columns([1, 1, 1])
with col1:
if st.button("📝 New Question", type="primary"):
st.session_state.quiz_question = quiz_gen.generate_question()
st.session_state.quiz_answer = None
st.session_state.quiz_submitted = False
st.session_state.show_explanation = False
with col2:
if st.button("💡 Show Explanation") and st.session_state.quiz_question:
st.session_state.show_explanation = True
with col3:
if st.button("🔄 Reset Quiz"):
st.session_state.quiz_question = None
st.session_state.quiz_answer = None
st.session_state.quiz_submitted = False
st.session_state.show_explanation = False
if st.session_state.quiz_question:
question = st.session_state.quiz_question
st.markdown("---")
st.subheader("Question:")
st.write(question["question"])
# Answer input
user_answer = st.number_input("Your answer:", value=0.0, format="%.2f", key="quiz_input")
if st.button("Submit Answer"):
st.session_state.quiz_answer = user_answer
st.session_state.quiz_submitted = True
# Check answer
if st.session_state.quiz_submitted and st.session_state.quiz_answer is not None:
correct_answer = question["answer"]
tolerance = question["tolerance"]
if abs(st.session_state.quiz_answer - correct_answer) <= tolerance:
st.success(f"✅ Correct! The answer is {correct_answer:.2f}")
st.balloons()
else:
st.error(f"❌ Not quite right. The correct answer is {correct_answer:.2f}")
st.write(f"Your answer: {st.session_state.quiz_answer:.2f}")
# Show explanation
if st.session_state.show_explanation:
st.markdown("---")
st.subheader("💡 Explanation:")
st.write(question["explanation"])
else:
st.info("Click 'New Question' to start the quiz!")
# Educational notes
st.sidebar.markdown("---")
st.sidebar.markdown("### 📚 Key Concepts")
st.sidebar.markdown("""
- **Magnitude**: Length of the vector
- **Direction**: Angle the vector makes
- **Components**: x and y parts of vector
- **Addition**: Tip-to-tail method
- **Resultant**: Sum of multiple vectors
""")
st.sidebar.markdown("### 💡 Try This")
st.sidebar.markdown("""
1. Set boat angle to 90° to go straight across
2. Increase current speed and watch the path change
3. Try launch angles of 45° for maximum range
4. Make two vectors perpendicular (90° apart)
5. Test the quiz mode to check your understanding
6. Change units to see the same physics in different measurements
""")
st.sidebar.markdown("### ⚙️ Features")
st.sidebar.markdown("""
- **Unit Conversion**: Change between m/s, km/h, mph, etc.
- **Error Analysis**: See how measurement uncertainty affects results
- **Quiz Mode**: Test your vector knowledge
- **Reset Button**: Restore default values
""") |