Acceleration of a rocket

Ritzycat

Homework Statement

A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0s later.

Homework Equations

$v_x = v_0 + at$
$x_f = x_0 + v_0t + 1/2at^2$
$v_x^2 = v_0^2 + 2a(Δx)$

The Attempt at a Solution

The biggest part I'm confused about is whether or not the bolt had an initial positive velocity (I am setting down as negative). It says the bolt "falls off the side", implying it just falls down.

Position of bolt before it falls
$0m = x + 1/2(-9.8m/s^2)(6.0s)^2$
$x_i = 176.4m$

Acceleration of rocket
$176.4m = 1/2(a)(4.0s)^2$
$a = 22.05 m/s^2$

Mentor
The biggest part I'm confused about is whether or not the bolt had an initial positive velocity (I am setting down as negative). It says the bolt "falls off the side", implying it just falls down.
The bolt will have the same velocity as the rocket at the moment it falls free. "Falls off the side" just means that it's not shot out or launched, but just let go.