The magnitude of the drag force of air resistance on a certain 20.0-kg object is proportional to its speed. If the object has a terminal speed 80.0 m/s, what is the magnitude of the drag force on the object when it is falling with a speed 30.0 m/s?

Question

anonymous · Answer

Drag force proportional to speed: 
Fd = kv ; k is some constant

We know at terminal velocity Vt: 
Fg = Fd
mg = kVt
k = mg / Vt = (20.0)(9.8)/(80.0) = 2.45 kg/s

Now we found the constant. We can use that to find the Fd at any speed.
Fd = kv = 2.45v
Fd = 2.45 (30.0) = 73.5 N

mrnood · Answer

@Pomeii00 has it just right for the question as set. (medal)

Just for general info - please note that drag is NOT normally proportional to the velocity - it is typically modelled as being proportional to velocity^2

the equation is given as:
$$F _{d}= \frac{ C _{d }\rho V ^{2}A }{2 }$$

Where 
Cd is coefficient of drag (depends on shape of body
rho is density of medium (e.g. air)
V is Velocity
A is representative area of body (e.g. cross section)

(this is just for reference - the question is fine....)