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A rocket sits initially at rest on the surface of the earth, until it begins burning...

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?

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