From Mechanics

The expression for the velocity \displaystyle \mathbf{v} has been obtained in part b).

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

If the aeroplane is travelling south this is in the negative \displaystyle \mathbf{j} direction.

If the aeroplane is travelling east this is in the positive \displaystyle \mathbf{i} direction.

Thus if the aeroplane is travelling south east the \displaystyle \mathbf{i} component of the velocity must equal the minus \displaystyle \mathbf{j} component of the velocity.

\displaystyle \begin{align} & 40=-(-2t) \\ & \\ & t=20\text{ s} \\ \end{align}