Question

The terminal velocity is not dependent on which one of the following properties? the drag coefficient 1 the force of gravity 2 cross-sectional area 3 air density 4 the falling time 5 terminal velocity depends on all of the 6 given parameters

Answer 1

Answer: the falling time

Explanation:

When a body or object falls, basically two forces act on it:  

1. The force of air friction, also called "drag force" $D$:  

$D={C}_{d}\frac{\rho V^{2} }{2}A$  (1)

Where:  

$C_ {d}$ is the drag coefficient  

$\rho$ is the density  of the fluid (air for example)

$V$ is the velocity  

$A$ is the transversal area of the object

So, this force is proportional to the transversal area of ​​the falling element and to the square of the velocity.  

2. Its weight due to the gravity force $W$:  

$W=m.g$

(2)

Where:  

$m$ is the mass of the object

$g$ is the acceleration due gravity  

So, at the moment when the drag force equals the gravity force, the object will have its terminal velocity:

$D=W$ (3)

${C}_{d}\frac{\rho V^{2} }{2}A=m.g$  (4)

$V=\sqrt{\frac{2m.g}{\rho A{C}_{d}}}$  (5) This is the terminal velocity

As we can see, there is no "falling time" in this equation.

Therefore, the terminal velocity is not dependent on the falling time.