This is derived from the equation:

Where:

• s is the distance
• u is the object's initial velocity
• a is the acceleration of the object
• t is the time

So for our apple while hanging from the branch it's initial velocity is 0, this clearly means that u multiplied by t must be 0 so this part of the equation can be ignored. The acceleration, a, is simply the acceleration due to gravity, g, which leaves the equation as:

Note that, as always with these equations, we ignore the effects of air resistance.