Answer
$F = [(1.7\times 10^4)~\hat{i}+0\hat{j} - (3.4\times 10^3)~\hat{k}]~N$
Work Step by Step
$\hat{r} = (0.020~m/s^3)~t^3~\hat{i}+(2.2~m/s)~t~\hat{j} - (0.060~m/s^2)~t^2~\hat{k}$
$v(t) = \frac{dr}{dt} = (0.060~m/s^3)~t^2~\hat{i}+(2.2~m/s)~\hat{j} - (0.120~m/s^2)~t~\hat{k}$
$a(t) = \frac{dv}{dt} = (0.120~m/s^3)~t~\hat{i}+0\hat{j} - (0.120~m/s^2)~\hat{k}$
At t = 5.0 s:
$a = (0.120~m/s^3)(5.0~s)~\hat{i}+0\hat{j} - (0.120~m/s^2)~\hat{k}$
$a = (0.600~m/s^2)~\hat{i}+0\hat{j} - (0.120~m/s^2)~\hat{k}$
We can find the mass of the helicopter.
$weight = mg$
$m = \frac{weight}{g} = \frac{2.75\times 10^5~N}{9.80~m/s^2}$
$m = 2.81\times 10^4~kg$
We can find the net force on the helicopter at t = 5.0 s.
$F = ma$
$F = (2.81\times 10^4~kg)[(0.600~m/s^2)~\hat{i}+0\hat{j} - (0.120~m/s^2)~\hat{k}]$
$F = [(1.7\times 10^4)~\hat{i}+0\hat{j} - (3.4\times 10^3)~\hat{k}]~N$
