Answer
The maximum acceleration the airplane can reach is $5.88\times10^{-3}m/s^2$
Work Step by Step
Considering the horizontal, we see that the man is under 2 forces: the propelling force $P$ to move him forward and static friction $f_s$. To start moving, $P$ has to surpass $f_s$. So,
$$P_{min}=f_s^{max}=\mu_sF_N$$
Since there is no vertical acceleration, we have $F_N=m_{man}g=85\times9.8=833N$
Therefore, $$P_{min}=0.77\times833=641.4N$$
This force $P$ to get the man to move is changed into tension $T$ in the cable to pull the airplane, so $T=641.4N$
Considering $m_{plane}=109000kg$, from Newton's 2nd law, the maximum acceleration the airplane can reach is $$a=\frac{T}{m_{plane}}=5.88\times10^{-3}m/s^2$$
