Why does a parachute decrease terminal velocity?

Question

Terminal Velocity depends on two things- surface area and speed. These are inversely proportionate.

If both these variables affect terminal velocity, why do parachutes slow you down? Initially you had a small surface area but a fast speed- with the parachute you have a larger surface area but lower speed. You have increased one variable but decreased the other. Therefore why do parachutes decrease speed?

Answer 1

You say:

Terminal Velocity depends on two things- surface area and speed

but I think you're getting slightly mixed up about the terminology. The drag (i.e. air resistance) depends on surface area and speed, but the terminal velocity is the speed and it just depends on the surface area (and air temperature, density, etc , etc that we'll assume is constant). You say;

with the parachute you have a larger surface area but lower speed

and this is quite correct but the speed is the terminal velocity so with the parachute you have a larger surface area but lower terminal velocity.

Answer 2

$(Drag) = (Coefficient)\times(Area)\times(Speed)^2 $

When $(Drag)=(Weight)$ then

$$ (Speed) = \sqrt{ \frac{ (Weight) } { (Coefficient)\times(Area) } } $$

So the larger the area the less the speed. What is the question again?