- In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
[In this question, \(\mathbf { i }\) is a unit vector due east and \(\mathbf { j }\) is a unit vector due north.
Position vectors are given relative to a fixed origin \(O\).]
At time \(t\) seconds, \(t \geqslant 1\), the position vector of a particle \(P\) is \(\mathbf { r }\) metres, where
$$\mathbf { r } = c t ^ { \frac { 1 } { 2 } } \mathbf { i } - \frac { 3 } { 8 } t ^ { 2 } \mathbf { j }$$
and \(c\) is a constant.
When \(t = 4\), the bearing of \(P\) from \(O\) is \(135 ^ { \circ }\)
- Show that \(c = 3\)
- Find the speed of \(P\) when \(t = 4\)
When \(t = T , P\) is accelerating in the direction of ( \(\mathbf { - i } - \mathbf { 2 7 j }\) ).
- Find the value of \(T\).