Question

a model rocket blasts off with a constant acceleration of 12.3m/s until it’s fuel runs out 10.2s later. It then enters free fall for the remainder of its flight. What is the total time the rocket was in the air?

Answer 1

$$h=0.5at^2=0.5(12.3)(10.2)^2=640\ m$$

$$0=h+vT-0.5gT^2\to 0=h+atT-0.5gT^2\\0=640+(12.3)(10.2)T-0.5(9.8)T^2\\T=30.0\ s$$

The  total time is

$$t+T=10.2+30=40.2\ s$$