Gravity & free fall

Let go of a pen and it falls to the floor. Every time. Whether in your room, on a mountain or on the other side of the world. The Earth pulls everything towards itself, including you. This attraction is called gravity, and it is behind every jump, every throw and every falling leaf.

Everything falls equally fast

A feather sails slowly to the ground, a hammer whizzes down. Is that because of weight? No, it is because of the air! Without air resistance, all objects fall equally fast, no matter how heavy they are. In 1971 the astronaut David Scott demonstrated this on the Moon: he released a feather and a hammer at the same time, and both landed in the moon dust at the same moment, because there is no air on the Moon.

Faster and faster: g ≈ 9.8 m/s²

We speak of free fall when only gravity acts and air resistance plays no role. An object released from rest then does not move at a constant speed, it accelerates: every second its speed grows by about 9.8 m/s. This number is called the acceleration due to gravity g, and its unit is m/s². After 1 s a falling stone is moving at about 9.8 m/s, after 2 s already at 19.6 m/s. As a formula: v = g · t. For rough estimates you may happily round g to 10 m/s².

How far does something fall?

Because the speed keeps growing, the distance fallen grows especially quickly. The formula is s = ½ · g · t². Using g ≈ 10 m/s²: after 1 s a stone has fallen about 5 m, after 2 s already 20 m, after 3 s a full 45 m. Double the time means four times the distance, because of the t². This lets you estimate the depth of a well, for example, by counting how long a stone takes to hit the bottom.