5 The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively. A helicopter moves horizontally with a constant acceleration of \(( - 0.4 \mathbf { i } + 0.5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\). At time \(t = 0\), the helicopter is at the origin and has velocity \(20 \mathrm { i } \mathrm { m } \mathrm { s } ^ { - 1 }\).

1. Write down an expression for the velocity of the helicopter at time \(t\) seconds.
2. Find the time when the helicopter is travelling due north.
3. Find an expression for the position vector of the helicopter at time \(t\) seconds.
4. When \(t = 100\) :
   1. show that the helicopter is due north of the origin;
   2. find the speed of the helicopter.