Two survey boats, A and B, move at constant velocities in a horizontal plane. Coordinates are measured in metres, with the $x$-axis pointing east and the $y$-axis pointing north. At $t=0$ their position vectors are

$$\mathbf r_A=(120,30), \qquad \mathbf r_B=(20,100),$$

and their velocity vectors are

$$\mathbf v_A=(3,1), \qquad \mathbf v_B=(5,-2),$$

in $\text{m s}^{-1}$ The time $t$ is measured in seconds.