1 The velocity of a model boat, \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { 1 }\), is given by $$\mathbf { v } = \binom { 5 } { 10 } + t \binom { 6 } { 8 }$$ where \(t\) is the time in seconds and the vectors \(\binom { 1 } { 0 }\) and \(\binom { 0 } { 1 }\) are east and north respectively.

1. Show that when \(t = 2.5\) the boat is travelling south-east (i.e. on a bearing of \(135 ^ { \circ }\) ). Calculate its speed at this time. The boat is at a point O when \(t = 0\).
2. Calculate the bearing of the boat from O when \(t = 2.5\).