6. The point \(A\) on a horizontal playground has position vector \(( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }\). At time \(t = 0\), a girl kicks a ball from \(A\). The ball moves horizontally along the playground with constant velocity \(( 4 \mathbf { i } + 5 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\). Modelling the ball as a particle, find

1. the speed of the ball,
2. the position vector of the ball at time \(t\) seconds. The point \(B\) on the playground has position vector \(( \mathbf { i } + 6 \mathbf { j } ) \mathrm { m }\). At time \(t = T\) seconds, the ball is due east of \(B\).
3. Find the value of \(T\). A boy is running due east with constant speed \(\nu \mathrm { ms } ^ { - 1 }\). At the instant when the girl kicks the ball from \(A\), the boy is at \(B\). Given that the boy intercepts the ball,
4. find the value of \(v\). \includegraphics[max width=\textwidth, alt={}, center]{5f2d38d9-b719-4205-8cb0-caa959afc46f-23_68_47_2617_1886}