3.14: Ship velocities and distance between ships

0606/21/M/J/22 — Question 8 · 7 marks

In this question,

\mathbf{i}

is due east and

\mathbf{j}

is due north. Distances are in kilometres and time in hours.

09\!00

, ship

A

leaves

P

with position vector

5\mathbf{i} + 16\mathbf{j}

and sails at constant speed

6\sqrt{3}

on a bearing of

120^{\circ}

(a)

Show that the velocity vector of

A

9\mathbf{i} - 3\sqrt{3}\,\mathbf{j}

[2]

(b)

Find the position vector of

A

12\!00

[1]

(c)

11\!00

ship

B

leaves

Q

with position vector

29\mathbf{i} + 16\mathbf{j}

and velocity

-12\sqrt{3}\,\mathbf{j}

. Write down the position vector of

B

t

hours after it starts sailing.

[1]

(d)

Find the distance between the two ships at

12\!00

[3]