A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity downward. a) what is the velocity of the rocket before it runs out of fuel? b) How long does it take to reach that point?

Answer: a) 88 m/s. b) 27 sec

Question

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s^2 until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity downward. a) what is the velocity of the rocket before it runs out of fuel? b) How long does it take to reach that point?

Answer: a) 88 m/s.   b) 27 sec

anonymous · Answer

Let's use the following equations. $$d = v_0 \cdot t + {1 \over 2} \cdot a \cdot t^2$$$$v = v_0 + a \cdot t$$We know the acceleration and altitude, therefore from the first equation, we can solve for the time of flight. This is the answer to part b. Plug this time back into the second equation to find the velocity after the fuel runs out.