The origin of the quadratic drag force on any projectile in a fluid is the inertia of the fluid that the projectile sweeps up. (a) assuming the projectile has a cross-sectional area a (normal to its velocity) and speed v, and that the density of the fluid is q, show that the rate at which the projectile encounters fluid (mass/time) is qa v. (b) making the simplifying assumption that all of this fluid is accelerated to the speed v of the projectile, show that the net drag force on the projectile is pit v 2 . it is certainly not true that all the fluid that the projectile encounters is accelerated to the full speed v, but one might guess that the actual force would have the form fquad = koav 2 ? (2.84) where k is a number less than 1, which would depend on the shape of the projectile, with k small for a streamlined body, and larger for a body with a flat front end. this proves to be true, and for a sphere the factor k is found to be k = 1/4. (c) show that (2.84) reproduces the form (2.3) for f quad, with c given by (2.4) as c = y d 2 . given that the density of air at stp is q = 1.29 kg/m 3 and that k = 1/4 for a sphere, verify the value of y given in (2.6).