4.05: Boat position vectors

0606/22/M/J/26 — Question 7 · 8 marks

Positions are measured in kilometres. At 13:00 boat \(A\) is at \(2\mathbf i+5\mathbf j\) and moves with velocity \(8\mathbf i+8\mathbf j\). At 15:00 boat \(B\) is at \(20\mathbf i+8\mathbf j\) and then travels on bearing \(300^\circ\) at speed \(5\sqrt3\) km h\(^{-1}\).

(a)

Find the position vector of \(A\) after \(2\) hours.

[1]

(b)

Write the position vector of \(A\) after \(t\) hours.

[1]

(c)

Find the position vector of \(B\) at 17:00.

[3]

(d)

Find the distance between the boats at 17:00.

[3]