Welcome to our physics lesson on free fall motion. Today we'll analyze a ball falling from the top of a tower. This is a fundamental problem in kinematics where we study motion under constant acceleration due to gravity. The ball starts from rest and accelerates downward at 9.8 meters per second squared.
Let's establish our initial conditions and coordinate system. The ball starts from rest, so initial velocity is zero. We place our origin at the top of the tower with positive direction pointing downward. The initial position is at height h, and gravity acts downward with acceleration of 9.8 meters per second squared. This setup allows us to apply kinematic equations systematically.
Now let's apply the kinematic equations for constant acceleration. We have three fundamental equations relating velocity, position, and time. Since our ball starts from rest with zero initial velocity, these equations simplify significantly. Velocity becomes simply g times t, position becomes one-half g t squared, and the velocity squared equals two g times the displacement. These simplified forms make calculations much easier.
Let's solve a specific example. A ball is dropped from a 45-meter tall tower. To find the time to hit the ground, we use the position equation: h equals one-half g t squared. Substituting our values: 45 equals one-half times 9.8 times t squared. Solving for t, we get approximately 3.03 seconds. The final velocity is g times t, which equals 29.7 meters per second. Watch the animation showing the ball's motion with real-time calculations.
Let's summarize the key insights from free fall motion. Distance increases quadratically with time, while velocity increases linearly. Importantly, the motion is independent of the object's mass - all objects fall at the same rate in a vacuum. These principles apply to many real-world situations including projectile motion, safety calculations in construction, engineering design, and sports physics. The graphs show how position follows a parabolic curve while velocity increases linearly, demonstrating the fundamental relationships in kinematics.