SUMMARY
The discussion centers on calculating the optimal angle for shooting a sword over a wall using a bow, given specific parameters. The wall height is 14 meters, and the sword weighs 1.28 kg, with a potential energy of 179 Nm available. The analysis reveals that the optimal launch angle can be calculated using the formula (π - atan(d/h))/2, where d is the horizontal distance (9 meters) and h is the height difference (11.6 meters). The naive solution of launching from 9 meters away yields a launch angle of approximately 71 degrees, while the optimal angle is lower, requiring less energy.
PREREQUISITES
- Understanding of projectile motion and trajectory analysis
- Familiarity with potential energy calculations
- Knowledge of the SUVAT equations for uniform acceleration
- Basic trigonometry, specifically the tangent and arctangent functions
NEXT STEPS
- Study the derivation of the optimal angle formula for projectile motion
- Learn about energy conservation in projectile motion scenarios
- Explore the SUVAT equations in detail for better understanding of motion analysis
- Practice solving similar physics problems involving angles and energy
USEFUL FOR
Physics students, educators, and anyone interested in understanding projectile motion and energy conservation principles in real-world applications.
