2. A rock is kicked from the top of a hill with an initial velocity vo making an angle 0 above the horizontal line. The hill is at an angle o below the horizontal as shown in the figure. -.-.- (a) Show that the rock hits the ground after a time 2vo sin(0 + 0) g cos o tf = (b) The rock falls a distance d down the hill (see figure). Show that this distance is given by [sin(20 + 26) + tan(4) (1 cos(20 + 20))]. g cos o d = (c) Show that the angle 0max that maximizes the distance d satisfies the relation tan(20max + 20) = cot o. Does this agree with what you know for the case o = 0? Note: Due to the properties of the arctan function, the above relation implies that 1 Omax = 90 o - arctan(cot ). (d) Find an expression for dmax if o = 30.