1. Derive the equations Vo X= " [1 - e-kt] (cos a) y= k [1 - e-kt] (sina) + Kz (1 - kt - e-kty by solving the following initial value problem for a vector r in the plane Differential equation: 742 = = -gj - kv = -gj - k -. r(0)=0 dr dt t=0 = vo = (vo cosa)i + (vo sin a)j The drag coefficient k is positive constant representing resistance due to air density, Vo and aare the projectile's initial speed and launch angle, and g is the acceleration due to gravity