Why do a heavy and a light object fall at the same rate when air resistance is ignored?

The larger weight of the heavy object is offset by its larger mass, so the acceleration is $g$ for both

A ball is thrown horizontally from a tabletop. What determines how long it stays in the air?

The height it falls (the vertical motion)

12questions. Pick an answer and you'll see why right away.

Which of these is a vector quantity?
A car drives 200 m east, then 200 m west, returning to its start. What is its displacement?
What is $72$ km/h expressed in meters per second?
A runner speeds up from $4.0$ m/s to $10$ m/s in $3.0$ s. What is the acceleration?
On a position-time graph, what does the slope of the line represent?
On a velocity-time graph, what does the area under the line represent?
An object starts from rest and accelerates at $3.0$ m/s squared for $4.0$ s. What is its final velocity?
Which kinematic equation gives displacement from initial velocity, acceleration, and time?
A ball is dropped from rest. Taking $g = 10$ m/s squared, how fast is it moving after $3.0$ s?
Why do a heavy and a light object fall at the same rate when air resistance is ignored?
A ball is thrown horizontally from a tabletop. What determines how long it stays in the air?
From the same height, one ball is dropped and another is thrown horizontally at the same instant. Which lands first?