# Model rocket - free fall acceleration again

missrikku
model rocket - free fall acceleration again :(

The problem states:

A model rocket fired vertically from the ground ascends with a constant vertical acceleration of 4.0 m/s^2 for 6.00 seconds. Its fuel is then exhausted, so it continues upward as a free-fall particle and then falls back down. a) what is the max altitude reached? b) what is the total time elapsed from takeoff until the rocket strikes the ground?

While drawing the sketch of this problem and attempting to solve part a, I got stuck when I was choosing the correct formulas to use.

To solve a, I tried to find the height of the rocket at t=6.0s

X-Xo = Vot + 0.5at^2

With R = height of the rocket at t = 6.0s,
R = Vot + 0.5(4.0)(6.0)^2 = (6.0)Vo + 72

My question is: would Vo = 0? I think I could solve this problem faster if that was the case. I was wondering about this because this rocket already had an acceleration of 4.0m/s^2 ti start and since acceleration is the change in velocity over time (right?) that must mean that there was some initial velocity so Vo doesn't equal 0. But if that's true, how would I go about finding that Vo? Do I even need that to solve this problem?

I was going to find the height of the rocket at t = 6.0s and then find the height from there up to the max using a = -g and Vmax = 0. Then the max height reached would be those values (height at 6.0s and height from there to the max height where Vmax = 0) added together.

Tom Mattson
Staff Emeritus
Gold Member

Originally posted by missrikku
To solve a, I tried to find the height of the rocket at t=6.0s

X-Xo = Vot + 0.5at^2

With R = height of the rocket at t = 6.0s,
R = Vot + 0.5(4.0)(6.0)^2 = (6.0)Vo + 72

OK

My question is: would Vo = 0?

Yes, you can assume that the rocket starts from rest.

Once you get the height at which the engine cuts out, remember that the only acceleration from that height onwards is the acceleration due to gravity.

enigma
Staff Emeritus
Gold Member

Originally posted by missrikku
and since acceleration is the change in velocity over time (right?) that must mean that there was some initial velocity so Vo doesn't equal 0.

Acceleration is change in velocity over time. That doesn't mean that you need a velocity to have an acceleration.

When the rocket is sitting on the pad, it has zero velocity. You then turn on the engine, and the engine provides the acceleration. The rocket still doesn't start moving until a split-second later (t just over 0).

HallsofIvy