In this question, time is in seconds.
At time \(t=0\), particle \(P\) starts from the point with position vector \(-30\mathbf j\).
\(P\) travels with speed \(58\text{ m s}^{-1}\) in the direction \(20\mathbf i+21\mathbf j\).
Find the position vector of \(P\) at time \(t\).[3]
Also at time \(t=0\), particle \(Q\) starts from the point with position vector \(-10\mathbf i+18\mathbf j\).
\(Q\) travels with speed \(75\text{ m s}^{-1}\) at an angle \(\alpha\) above the positive \(x\)-axis, where \(\tan\alpha=\dfrac7{24}\).
Find the position vector of \(Q\) at time \(t\).[4]
Determine whether \(P\) and \(Q\) collide.[2]