To understand the effect of air resistance on the motion of a bullet let's consider a bullet of the shape shown in the fig. The bullet is flying horizontally. The cross section of cylindrical part is A and the conical part has a semi vertical angle of `45^(@)`. Assume that the bullet is fired with initial velocity `u` and moves in a gaseous medium in which molecules are at rest (do you think this assumption is necessary?). Collisions of the molecules with the bullet are elastic. Take mass of bullet to be M, density of gaseous medium as `rho` and disregard gravity.

(a) Consider two bullets one small and other large, made of same material. Which will experience larger retardation due to air resistance ?
(b) Write the speed of bullet after time t
(c) Write distance travelled by the bullet in time t.

Answer

(a) Smaller bullet
(b) `(Mu)/(M + rho A ut)`
(c) `(M)/(rhoA)l n[1+(rhoAu)/(M)t]`