A model rocket is launched straight upward
with an initial speed of 48.3 m/s. It acceler-
ates with a constant upward acceleration of
2.23 m/s2 until its engines stop at an altitude
of 160 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
Answer in units of m

Question

A model rocket is launched straight upward
with an initial speed of 48.3 m/s. It acceler-
ates with a constant upward acceleration of
2.23 m/s2 until its engines stop at an altitude
of 160 m.
What is the maximum height reached by
the rocket? The acceleration of gravity is
9.81 m/s2.
Answer in units of m

anonymous · Answer

There are two steps to this problem: 
1. The stage when the rocket is accelerating upward.
2. The stage after the rocket reaches 160 m.

In the first stage, they tell you the altitude it reaches, so clearly you don't need to calculate that. What you do need to calculate is its final velocity, as that is needed to determine how much further it travels after its rockets turn off. The velocity equation you need for stage 1 is $$v _{f} = v _{0} + at$$ Do you have an idea where to go from here?