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phospho

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A coastguard station O monitors the movements 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 (−3i+10j)km relative to O and has velocity (2i+2j)kmh−1. Ship B is at the point with position vector (6i+j)km and has velocity (−i+5j)kmh−1.

a Show that if the two ships maintain these velocities they will collide.

The coastguard radios ship A and orders it to reduce its speed to move with velocity (i+j)kmh−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 three significant figures, the distance between A and B at 1500 hours,

d find the time at which B will be due north of A.

**a) done**

b) (9-2t)i + (-9+4t)j done

c) done

d) I'm not sure how to do this but I thought if B will be due north of A, then the i components should be the same no? so I done this i.e 10+t = 16 => t = 6 however this is wrong and in the solutions they say that the i component should be equal to 0, however in the next question:

b) (9-2t)i + (-9+4t)j done

c) done

d) I'm not sure how to do this but I thought if B will be due north of A, then the i components should be the same no? so I done this i.e 10+t = 16 => t = 6 however this is wrong and in the solutions they say that the i component should be equal to 0, however in the next question:

Two ships P and Q are moving along straight lines with constant velocities. Initially P is at a point O and the position vector of Q relative to O is (12i+6j)km, where i and j are unit vectors directed due east and due north respectively. Ship P is moving with velocity 6ikmh−1 and ship Q is moving with velocity (−3i+6j)kmh−1. At time t hours the position vectors of P and Q relative to O are p km and q km respectively.

a Find p and q in terms of t.

b Calculate the distance of Q from P when t=4.

c Calculate the value of t when Q is due north of P.

Part c) they say that it's when the i components are equal, which is what I done for the first question.

Could anyone explain what is going on?

Part c) they say that it's when the i components are equal, which is what I done for the first question.

Could anyone explain what is going on?