Answer
The apparent weight of the astronaut is $729.6N$.
Work Step by Step
1) Find the acceleration $a$ of the rocket
We have initial velocity $v_0=0$, final velocity $v=45m/s$ and time to reach that velocity $\Delta t=15s$. Therefore, $$v=v_0+at$$ $$a=\frac{v-v_0}{\Delta t}=3m/s^2$$
2) The apparent weight of the astronaut is calculated according to the formula $$F_N=mg+ma=m(g+a)$$
where $m$: mass of the astronaut, $g$: gravitational acceleration on earth, $a$: acceleration of the rocket
$$F_N=57(9.8+3)=729.6N$$
