Answer to Question #257726 in Math for Mohammed

Question

A particle is subject to uniform gravity and the linear resistance force -mKv, where K is a positive constant and v is the velocity of the particle. Initially the particle is projected with speed $\mu$ in a direction making an angle $\alpha$ with the horizontal.

(a). Find the vector equation of motion and the corresponding scalar equations of motion.

(b). Show that the solution for the trajectory of the particle at t=0,z=0,x=0 is x=$\mu$cos$\alpha$ /K (1-e^-Kt) z=K$\mu$sin$\alpha$+g/K² (1-e^-Kt)-g/K t

(c). Find an approximate formula for the range on level ground when the resistance parameter $\lambda$=K$\mu$/g is small.