From Mechanics

The expression for the position vector \displaystyle \mathbf{r} has been obtained in part b).

\displaystyle \mathbf{r}=\left( 40t \right)\mathbf{i}+\left( {-{t}^{2}}+400 \right)\mathbf{j}

If the aeroplane is due east of the origin its position in the north-south direction must be zero, which means the \displaystyle \mathbf{j} component of the position vector must be zero.

\displaystyle \begin{align} & {-{t}^{2}}+400=0 \\ & \\ & t=20\text{ s} \\ \end{align}