3. The height h of an object t seconds after being released can be modeled by the equation: h(t)= -1/2at^2 +vt + s
where a is the acceleration due to gravity, v is the upward speed of the object upon release,
and s is the starting height of the object. (If the object starts on earth, then s = 0.) At the
surface of the earth, acceleration a = 32 ft/s2. A model rocket is launched from the top of a
cliff that is 384 feet high with an upward speed of 160 ft/s.
(a) Write a specific function that represents the height of the rocket as a function of time.

(b) How many seconds after the launch does the rocket reach its maximum height?

(c) Determine the maximum height attained by the rocket (to the nearest foot)

(d) How many seconds after the launch does the rocket reach the ground?