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# mechanics vectors watch

1. 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) km/h. Ship B is at the point with position vector (6i+j) km and has velocity (-i+5j) km/h.

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) km/h. Given the A obeys this order and maintains this new constant velocity:

b) find an expression for the vector AB for 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.
I got part a and part b, but i dont know how to start part c, can someone help me ?
2. Well you have an expression for the vector ab as a function of time yes? How could you use that in the context of this question
3. (Original post by alesha98)
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) km/h. Ship B is at the point with position vector (6i+j) km and has velocity (-i+5j) km/h.

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) km/h. Given the A obeys this order and maintains this new constant velocity:

b) find an expression for the vector AB for 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.
I got part a and part b, but i dont know how to start part c, can someone help me ?
You've done part (b)

So you know you can write AB = f(t)i + g(t)j - no?

Now plug t = 3 (that's 3 hours after noon, so 15:00 hours) then you'll get AB = number * i + other number * j

Now compute the length of this vector using sqrt(number^2 + other number^2)
4. (Original post by Zacken)
You've done part (b)

So you know you can write AB = f(t)i + g(t)j - no?

Now plug t = 3 (that's 3 hours after noon, so 15:00 hours) then you'll get AB = number * i + other number * j

Now compute the length of this vector using sqrt(number^2 + other number^2)
ah thankyou. i thought i need to sub t = 1500 ... because there wasnt a colon between
5. (Original post by alesha98)
ah thankyou. i thought i need to sub t = 1500 ... because there wasnt a colon between
No problemo, glad I helped. They like referring to times without colons, you should get used to it. :-)

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