A rocket sits initially at rest on the surface of the earth,
until it begins burning its engines. While burning its engines, it
accelerates upward at 30.0 m/s2 for 30.0 s. It then runs
out of fuel and continues ascending to its maximum height in free
fall. Ignoring air resistance, (i) what is the rocket’s maximum
altitude, and (ii) how much time passes from liftoff to reaching
its maximum altitude?