Final answer:
Including drag in projectile motion decreases both the maximum height and range of the projectile due to the opposing force acting on the horizontal and vertical components. Without air resistance, the optimal launch angle is 45 degrees, but with drag, it's about 38 degrees. The initial velocity and gravity also significantly impact the range.
Step-by-step explanation:
When drag is included in projectile motion, the height and range of the projectile are affected. Drag, or air resistance, acts in the opposite direction of the projectile's motion, thus decreasing both its horizontal and vertical components of velocity. As a consequence, the projectile will reach a lower maximum height compared to when drag is negligible. Additionally, the horizontal distance covered by the projectile, known as the range, is also reduced because the horizontal component of the velocity is decelerated more quickly due to the presence of drag.
In the absence of air resistance, the maximum range of a projectile is achieved at an initial launch angle of 45 degrees. However, with drag considered, the optimal angle is slightly less, approximately 38 degrees. Importantly, the initial velocity has a significant impact on the range—the greater the initial velocity, the farther the projectile will travel. Furthermore, the acceleration of gravity also affects the range; on the Moon, where gravity is weaker, the range would be greater, as experienced by astronaut Alan Shepherd.