SUMMARY
The problem involves calculating the launch angle of a ball thrown with an initial velocity of 20 m/s towards a wall 50 meters away, starting from a height of 1.8 meters and hitting the wall at a height of 1.2 meters. The key equations used are 50 = 20t*cos(theta) and -0.6 = 20t*sin(theta) - 0.5(9.8)(t^2). By rearranging the first equation to solve for time (t) and substituting it into the second equation, the angle (theta) can be determined without directly calculating the time.
PREREQUISITES
- Understanding of projectile motion principles
- Familiarity with trigonometric functions and their applications in physics
- Knowledge of basic kinematic equations
- Ability to manipulate algebraic equations
NEXT STEPS
- Study projectile motion equations in detail
- Learn how to derive time of flight in projectile problems
- Explore the use of trigonometric identities in physics
- Practice solving similar problems involving angles and heights
USEFUL FOR
Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators looking for examples of applying kinematic equations in real-world scenarios.