I encountered a question involving air resistance and it begins by giving a formula: "The force of air resistance is roughly proportional to the square of an object's speed and is directed opposite to the velocity: F(air) = -cv^2, where c is a constant that depends largely on the shape of the falling body..........." For F(air) = -cv^2 , is there a FLAW in the structure of the formula itself? Is there any valid reason to introduce the negative sign? I used the given formula to find the acceleration of a 80kg skydiver falling at 25m/s (with c=0.5 Ns^2/m^2) to be -13.7m/s^2 which is crazy... -cv^2 -mg = ma Substituing the given values gives a=-13.7m/s^2 c>0 and v^2 >0, so the formula automatically negatives the air resistance and this means air resistance always point downward...which is wrong If the formula is trying to say air resistance is directed opposite to velocity, this is nonsense as well because (-30m/s)^2 and (30m/s)^2 gives the same thing and the negative sign in front of cv^2 does nothing to show that they have opposite directions. What should be the correct way of stating this formula? | F(air) | = cv^2 ?? How about in vector form?