Answer
(a) $64s$
(b) $113512ft$
(c) $16384ft$
Work Step by Step
(a) Step 1. List the given parametric equations: $x=(v_0cos\alpha)t, y=(v_0sin\alpha)t-16t^2$
Step 2. With the initial conditions $v_0=2048ft/s, \alpha=30^{\circ}$, let $y(t)=0$ for the moment when the bullet hit the ground, we have $2048sin30^{\circ}t-16t^2=0$ which gives $t=64s$ (we throw away t=0 as it is the starting point.)
(b) The total distance is given by the x-value at t=64s: $x=2048cos30^{\circ}\times64\approx113512ft$
(c) The maximum height is reached at half of the total travel time $t1=\frac{64}{2}=32s$ which gives
$y=2048sin30^{\circ}\times32-16\times32^2=16384ft$
