- #1

**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.