7. Two cars \(A\) and \(B\) are moving on straight horizontal roads with constant velocities. The velocity of \(A\) is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) due east, and the velocity of \(B\) is \(( 10 \mathbf { i } + 10 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors directed due east and due north respectively. Initially \(A\) is at the fixed origin \(O\), and the position vector of \(B\) is \(300 \mathbf { i }\) m relative to \(O\). At time \(t\) seconds, the position vectors of \(A\) and \(B\) are \(\mathbf { r }\) metres and \(\mathbf { s }\) metres respectively.

1. Find expressions for \(\mathbf { r }\) and \(\mathbf { s }\) in terms of \(t\).
2. Hence write down an expression for \(\overrightarrow { A B }\) in terms of \(t\).
3. Find the time when the bearing of \(B\) from \(A\) is \(045 ^ { \circ }\).
4. Find the time when the cars are again 300 m apart. END