A projectile of mass 200 g is launched in a viscous medium at an angle 60^ with the horizontal, with an initial velocity of 270 ~m / s . It experiences a viscous drag force F =-c v where the drag coefficient c=0.1 ~kg / s and v is the instantaneous velocity of the projectile. The projectile hits a vertical wall after 2 s . Taking e=2.7 , the horizontal distance of the wall from the point of projection (in m ) is

Step-by-step solution

F _ net = m ~d v dt mg + F = md v dt mg - C v = md v dt Horizontal direction - Cv _ x = mdv _ x dt aligned & - C m ₀^t d t= _ v_ 0 x ^ v_x d v_x v_x & - t 2 = n v_x v_ 0 x & d x d t =v_x=v_ 0 x e^ -t / 2 & ₀^ S_x d x=v_ 0 x ₀^t e^ -t / 2 d t & S_x=2 v_ 0 x (1-e^ -t / 2 ) & at t=2 aligned aligned & S _ x =2 270 60^ [1- 1 e ] & S _ x =270 (1- 1 2.7 ) & = 270 2.7 (1.7) & =170 ~m & ~S _ x =170 ~m aligned