Answer
$1.90\times10^5\;\rm N$
Work Step by Step
In this case, the net force exerted on the jet plane in the $x$-direction is given by
$$\sum F_x=F_{Thrust}-f_r=ma_x$$
Air resistance is negligible but not the rolling friction as the author told us.
Solving for the thrust force;
$$F_{Thrust}= ma_x+f_r$$
Rolling friction is given by $f_r=\mu_rF_n$
$$F_{Thrust}=ma_x+\mu_r F_n \tag 1$$
In this case, the net force exerted on the jet plane in the $y$-direction is given by
$$\sum F_y=F_{n}-mg=ma_y=m(0)=0$$
Thus,
$$F_n=mg$$
Plugging into (1);
$$F_{Thrust}=ma_x+\mu_r mg $$
$$F_{Thrust}=m\left[a_x+\mu_r g\right] \tag 2 $$
Now we need to find the plane's acceleration, we know it starts from rest and reaches a speed of 82 m/s during a time interval of 35 s.
Thus,
$$v_{x}=\overbrace{v_{ix}}^{0}+a_xt$$
Thus,
$$a_x=\dfrac{v_x}{t} $$Plugging into (2);
$$F_{Thrust}=m\left[\dfrac{v_x}{t} +\mu_r g\right] $$
Plugging the known;
$$F_{Thrust}=75000\left[\dfrac{82}{35} +(0.02\cdot 9.8) \right] $$
$$F_{Thrust}=\color{red}{\bf 1.90\times10^5}\;\rm N$$
