1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors due east and due north respectively]

A radio controlled model boat is placed on the surface of a large pond.
The boat is modelled as a particle.
At time \(t = 0\), the boat is at the fixed point \(O\) and is moving due north with speed \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Relative to \(O\), the position vector of the boat at time \(t\) seconds is \(\mathbf { r }\) metres.
At time \(t = 15\), the velocity of the boat is \(( 10.5 \mathbf { i } - 0.9 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
The acceleration of the boat is constant.

1. Show that the acceleration of the boat is \(( 0.7 \mathbf { i } - 0.1 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\).
2. Find \(\mathbf { r }\) in terms of \(t\).
3. Find the value of \(t\) when the boat is north-east of \(O\).
4. Find the value of \(t\) when the boat is moving in a north-east direction.