# Question #5a5fa

Feb 16, 2017

Because of air resistance

#### Explanation:

You need to account for air resistance (or drag). In the absence of air resistance, objects will accelerate at the same rate, so two objects dropped simultaneously from the same height will reach the floor at the same time.

Air resistance complicates matters. This force opposes motion and increases with surface area and velocity. Mathematically it can be expressed as:

$\text{Air resistance" = "Constant" times "area} \times v e l o c i t {y}^{2}$
$A R = k A {v}^{2}$

An object will reach its terminal velocity when its weight is balanced by the air resistance. So

$m g = k A {v}^{2}$

Hence the terminal velocity is given by

$v = \sqrt{\frac{m g}{k A}}$

Hence the ratio of mass to area is the critical factor in determining terminal velocity. For the paper, this ratio would be very small and for the computer it would be much larger.

Hence the paper will reach its terminal velocity much more quickly and it will be much lower than the laptop. Hence the laptop hits the ground first