Answer
The bullet's speed relative to the Earth is $~~0.357~c~~$ in the opposite direction from the rocket's motion.
Work Step by Step
Let $u'$ be the bullet's velocity relative to the rocket.
Let $v$ be the rocket's velocity relative to the Earth.
Let $u$ be the bullet's velocity relative to the Earth.
We can find $u$:
$u = \frac{u'+v}{1+\frac{u'v}{c^2}}$
$u = \frac{-0.9c+0.8c}{1+\frac{(-0.9c)(0.8c)}{c^2}}$
$u = \frac{-0.1c}{1-0.72}$
$u = -0.357~c$
The bullet's speed relative to the Earth is $~~0.357~c~~$ in the opposite direction from the rocket's motion.
