M1 vectors Q! Please hlep!

The horizontal vectors i and j are directed due East and North.

A coastguard station O monitors the movement of ships in a channel. At noon, the station's radar records two ships moving with constant speed. Ship A is at the point with position vector (-5i+10j)km relative to O and has velocity (2i+2j)km h^-1. Ship B is at the point with position vector (3i+4j) and has velocity (-2i+5j)km h^-1.
a) Given that the two ships maintain these velocities, show that they collide.
The coast guard radios ship A and orders it to reduce its speed to move with velocity (i+j)km h^-1.
Given that A obeys this order and maintains this new constant velocity,
b) find an expression for the vector AB at time t hours after noon.
c) find, to 3 sig figs, the distance between A and B at 1400 hours.
d) find the time at whcih B will be due north of A.

Reply 1

Eddie K

For part a) What do you know about the position vectors at time t for both ships if the two ships collide? Remember, r' = r + vt.

For part b) What have you learnt from part a) that you can apply here? Remember the basics of vector addition.

For part c) What is the distance (length) between A and B in terms of the vectors OA and OB? You will already have vector equations for the position vector of each vector at any time t, can you use these?

For part d) What will the position vector of B be when it is exactly North of A? Will the vector A-B have any component due East? Which of your equations can you use to find the time?

Use these hints and you will be able to crack the question!