A ball is thrown from a building at an angle, landing 50 meters away after 5 seconds, with a maximum height of 20 meters above the roof. The discussion focuses on calculating the initial velocity and launch angle, using the horizontal and vertical components of motion. Key equations include those for maximum height and range, leading to the determination of horizontal speed as 10 m/s. The vertical component is derived from the maximum height, resulting in an initial vertical velocity of approximately 19.79 m/s. Ultimately, the launch angle is calculated to be 63 degrees after correcting for radians.