Answer:
[tex]16819.57185\hat{i}+3363.91437\hat{j}[/tex]
Explanation:
The position vector is
[tex]\vec{r}=0.02t^3\hat{i}+2.2t\hat{j}+0.06t^2\hat{k}[/tex]
Differentiating with respect to time
[tex]v=\dfrac{d}{dt}0.02t^3\hat{i}+2.2t\hat{j}+0.06t^2\hat{k}\\\Rightarrow v=0.06t^2\hat{i}+2.2\hat{j}+0.12t\hat{k}[/tex]
Differentiating with respect to time
[tex]a=\dfrac{dv}{dt}\\\Rightarrow a=\dfrac{d}{dt}0.06t^2\hat{i}+2.2\hat{j}+0.12t\hat{k}\\\Rightarrow a=0.12t\hat{i}+0.12\hat{k}[/tex]
Mass of the helicopter
[tex]m=\dfrac{W}{g}\\\Rightarrow m=\dfrac{2.75\times 10^5}{9.81}\\\Rightarrow m=28032.6197757\ kg[/tex]
Net force on the helicopter
[tex]F=ma\\\Rightarrow F=28032.6197757(0.12t\hat{i}+0.12\hat{k})\\\Rightarrow F=3363.91437\hat{i}t+3363.91437\hat{j}[/tex]
At t = 5 s
[tex]F=3363.91437\hat{i}\times 5+3363.91437\hat{j}\\\Rightarrow F=16819.57185\hat{i}+3363.91437\hat{j}[/tex]
The force is [tex]16819.57185\hat{i}+3363.91437\hat{j}[/tex]
