Projectile motion is a fundamental concept in physics where an object moves in a curved path under the influence of gravity. Common examples include airplanes dropping bombs and balls hitting inclined surfaces. The motion combines constant horizontal velocity with accelerating vertical motion due to gravity.
Projectile motion can be analyzed by separating it into horizontal and vertical components. Horizontally, the object moves with constant velocity, following x equals v-zero times t. Vertically, the object accelerates downward due to gravity, with position y equals one-half g t squared and velocity v-y equals g t. The combination creates a parabolic trajectory.
In the airplane bombing problem, we analyze how far a bomb travels horizontally when dropped from a moving aircraft. The time of flight depends only on the height, given by t equals square root of 2h over g. The horizontal range is the initial velocity times this flight time, resulting in R equals v-zero times square root of 2h over g.