Question 745513
Indeed we use the given equation

s(t)=-16t^2+150t+2

a) when will rocket reach 300 ft
   300 = -16t^2 + 150t + 2
   -16t^2 + 150t - 298 = 0
   use quadratic formula to solve
   t = -150 plus or minus sqrt(150^2 - 4(-16)-298) / (-16*2)

b) note if t = 0 then s = 2  which is the initial distance

c) when will it reach the ground
   to answer this we use the first derivative which is
   -32t+150 and
    t <75/16
    so the rocket has a maximum height at (75/16, s(75/16))
    now we want to know when it will reach the ground, this is just
    2 * 75/16 or 75/8 = 9.38 seconds

a nifty free math calculator program for windows is "speedcrunch"  :-)